AAAA
FILE INFORMATION
FILENAME(S): AAAA
FILE TYPE(S): PRG
FILE SIZE: 35.2K
FIRST SEEN: 2025-11-30 16:59:42
APPEARS ON: 1 disk(s)
FILE HASH
f11ff4bf1252944f4b9d5e97cf36b8dfecfee6a5830369a42d10f1c48f28d0c6
FOUND ON DISKS (1 DISKS)
| DISK TITLE | FILENAME | FILE TYPE | COLLECTION | TRACK | SECTOR | ACTIONS |
|---|---|---|---|---|---|---|
| MATHS TUTOR 1 | AAAA | PRG | High Voltage Complete C64 Collection | 27 | 0 | DOWNLOAD FILE |
FILE CONTENT & ANALYSIS
> DETECTED: COMMODORE BASIC PROGRAM (LOAD ADDRESS $0801)
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00001F80: 20 12 32 92 20 49 53 20 43 4F 52 52 45 43 54 2E | .2. IS CORRECT.|
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00001FA0: 32 11 2B 42 58 2B 43 20 48 41 53 20 46 41 43 54 |2.+BX+C HAS FACT|
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00001FC0: 57 48 45 52 45 22 3A 99 3A 99 00 FE 27 54 29 99 |WHERE":.:...'T).|
00001FD0: 22 20 50 51 3D 43 2C 20 53 4F 20 49 4E 20 32 58 |" PQ=C, SO IN 2X|
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00001FF0: 20 4C 45 54 27 53 20 4C 4F 4F 4B 22 3A 99 00 36 | LET'S LOOK":..6|
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00002010: 53 45 43 54 49 4F 4E 20 41 47 41 49 4E 2E 20 9B |SECTION AGAIN. .|
00002020: 57 52 49 54 45 20 44 4F 57 4E 20 54 48 45 22 3A |WRITE DOWN THE":|
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00002040: 00 6A 28 68 29 97 31 39 38 2C 30 3A 85 20 22 20 |.j(h).198,0:. " |
00002050: 20 20 41 4E 44 20 41 51 2B 50 20 3D 20 12 D2 22 | AND AQ+P = .."|
00002060: 3B 42 31 24 3A 99 22 92 93 22 00 7D 28 72 29 8B |;B1$:."..".}(r).|
00002070: 42 31 24 B2 22 33 22 89 31 30 36 35 30 00 B1 28 |B1$."3".10650..(|
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000020A0: 20 49 53 20 43 4F 52 52 45 43 54 2E 22 3A 99 3A | IS CORRECT.":.:|
000020B0: 99 00 E6 28 86 29 99 22 20 41 58 91 32 11 2B 42 |...(.)." AX.2.+B|
000020C0: 58 2B 43 20 48 41 53 20 46 41 43 54 4F 52 53 20 |X+C HAS FACTORS |
000020D0: 28 41 58 2B 51 29 28 58 2B 50 29 20 57 48 45 52 |(AX+Q)(X+P) WHER|
000020E0: 45 22 3A 99 3A 99 00 1A 29 8B 29 99 22 20 41 51 |E":.:...).)." AQ|
000020F0: 2B 50 3D 42 2C 20 53 4F 20 49 4E 20 32 58 91 32 |+P=B, SO IN 2X.2|
00002100: 11 2B 33 58 2B 32 2C 20 41 51 2B 50 3D 12 33 92 |.+3X+2, AQ+P=.3.|
00002110: 2E 20 57 45 27 4C 4C 22 3A 99 00 52 29 90 29 99 |. WE'LL":..R).).|
00002120: 22 20 52 45 56 49 45 57 20 54 48 49 53 20 50 41 |" REVIEW THIS PA|
00002130: 52 54 2E 20 9B 50 4C 45 41 53 45 20 57 52 49 54 |RT. .PLEASE WRIT|
00002140: 45 20 44 4F 57 4E 20 54 48 45 22 3A 89 31 30 30 |E DOWN THE":.100|
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000021A0: 54 49 4F 4E 3A 9A 22 3A 99 00 E1 29 B8 29 99 22 |TION:.":...).)."|
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000021C0: 53 49 4E 43 45 20 41 20 49 53 20 41 20 50 52 49 |SINCE A IS A PRI|
000021D0: 4D 45 20 4E 55 4D 42 45 52 11 22 3A 8D 38 35 31 |ME NUMBER.":.851|
000021E0: 30 00 14 2A C2 29 99 22 9F 32 9A 20 28 32 58 9B |0..*.).".2. (2X.|
000021F0: 2B 9A 20 29 28 58 9B 2B 9A 20 29 20 53 49 4E 43 |+. )(X.+. ) SINC|
00002200: 45 20 42 3D 9B 2B 9A 35 20 26 20 43 3D 9B 2B 9A |E B=.+.5 & C=.+.|
00002210: 32 22 3A 99 00 1E 2A C7 29 8D 38 35 31 30 00 53 |2":...*.).8510.S|
00002220: 2A CC 29 99 22 9F 33 9A 20 28 32 58 9B 2B 31 9A |*.).".3. (2X.+1.|
00002230: 29 28 58 9B 2B 32 9A 29 20 53 49 4E 43 45 20 43 |)(X.+2.) SINCE C|
00002240: 3D 50 51 3D 28 32 29 28 31 29 3D 32 20 41 4E 44 |=PQ=(2)(1)=2 AND|
00002250: 22 3A 99 00 84 2A D6 29 99 22 20 20 20 20 20 20 |":...*.)." |
00002260: 20 20 20 20 20 20 20 20 20 20 20 20 20 20 42 3D | B=|
00002270: 41 51 2B 50 3D 28 32 29 28 32 29 2B 31 3D 35 22 |AQ+P=(2)(2)+1=5"|
00002280: 3A 99 3A 99 00 8E 2A DB 29 8D 38 35 31 30 00 BA |:.:...*.).8510..|
00002290: 2A E0 29 99 22 20 4E 4F 57 20 59 4F 55 20 54 52 |*.)." NOW YOU TR|
000022A0: 59 2C 20 46 41 43 54 4F 52 49 53 45 20 33 58 91 |Y, FACTORISE 3X.|
000022B0: 32 11 2B 37 58 2B 32 22 3A 99 00 E1 2A EA 29 97 |2.+7X+2":...*.).|
000022C0: 31 39 38 2C 30 3A 85 20 22 20 12 28 D2 D2 D2 D2 |198,0:. " .(....|
000022D0: 29 28 D2 D2 D2 29 22 3B 42 31 24 3A 99 22 92 93 |)(...)";B1$:."..|
000022E0: 22 00 18 2B F4 29 43 31 24 B2 22 28 33 58 2B 31 |"..+.)C1$."(3X+1|
000022F0: 29 28 58 2B 32 29 22 3A 8B 42 31 24 B2 43 31 24 |)(X+2)":.B1$.C1$|
00002300: B0 42 31 24 B2 22 28 58 2B 32 29 28 33 58 2B 31 |.B1$."(X+2)(3X+1|
00002310: 29 22 89 31 30 37 38 30 00 40 2B F9 29 43 32 24 |)".10780.@+.)C2$|
00002320: B2 22 33 58 91 32 11 2B 36 58 2B 58 2B 32 22 3A |."3X.2.+6X+X+2":|
00002330: 43 33 24 B2 22 33 58 91 32 11 2B 37 58 2B 32 22 |C3$."3X.2.+7X+2"|
00002340: 00 4F 2B FA 29 8B 52 B2 31 89 31 30 37 35 30 00 |.O+.).R.1.10750.|
00002350: 59 2B FC 29 8D 39 31 30 30 00 68 2B FD 29 52 B2 |Y+.).9100.h+.)R.|
00002360: 31 3A 89 31 30 37 32 30 00 8C 2B FE 29 99 22 20 |1:.10720..+.)." |
00002370: 4E 4F 2C 20 22 42 31 24 22 20 49 53 20 53 54 49 |NO, "B1$" IS STI|
00002380: 4C 4C 20 57 52 4F 4E 47 2E 22 3A 99 00 B1 2B 08 |LL WRONG.":...+.|
00002390: 2A 99 22 20 12 22 43 31 24 22 92 20 49 53 20 52 |*." ."C1$". IS R|
000023A0: 49 47 48 54 2E 20 22 43 31 24 22 3D 22 3A 99 3A |IGHT. "C1$"=":.:|
000023B0: 99 00 D0 2B 12 2A 99 22 20 22 43 32 24 22 20 3D |...+.*." "C2$" =|
000023C0: 20 22 43 33 24 22 2E 20 4C 45 54 27 53 22 3A 99 | "C3$". LET'S":.|
000023D0: 00 06 2C 17 2A 99 22 20 47 4F 20 4F 56 45 52 20 |..,.*." GO OVER |
000023E0: 54 48 49 53 2E 20 9B 50 4C 45 41 53 45 20 57 52 |THIS. .PLEASE WR|
000023F0: 49 54 45 20 44 4F 57 4E 20 54 48 45 22 3A 99 3A |ITE DOWN THE":.:|
00002400: 89 31 30 30 35 30 00 10 2C 1C 2A 8D 39 30 36 30 |.10050..,.*.9060|
00002410: 00 3C 2C 26 2A 99 22 20 9F 45 58 41 4D 50 4C 45 |.<,&*." .EXAMPLE|
00002420: 20 32 3A 9A 20 46 41 43 54 4F 52 49 53 45 20 33 | 2:. FACTORISE 3|
00002430: 58 91 32 11 2D 37 58 2B 32 22 3A 99 00 52 2C 30 |X.2.-7X+2":..R,0|
00002440: 2A 99 22 20 9F 53 4F 4C 55 54 49 4F 4E 3A 9A 22 |*." .SOLUTION:."|
00002450: 3A 99 00 85 2C 3A 2A 99 22 9F 31 9A 20 28 33 58 |:...,:*.".1. (3X|
00002460: 20 20 29 28 58 20 20 29 20 53 49 4E 43 45 20 41 | )(X ) SINCE A|
00002470: 20 49 53 20 41 20 50 52 49 4D 45 20 4E 55 4D 42 | IS A PRIME NUMB|
00002480: 45 52 22 3A 99 00 8F 2C 3F 2A 8D 38 35 31 30 00 |ER":...,?*.8510.|
00002490: C4 2C 44 2A 99 22 9F 32 9A 20 28 33 58 9B 2D 9A |.,D*.".2. (3X.-.|
000024A0: 20 29 28 58 9B 2D 9A 20 29 20 53 49 4E 43 45 20 | )(X.-. ) SINCE |
000024B0: 42 3D 9B 2D 9A 37 20 9B 26 9A 20 43 3D 9B 2B 9A |B=.-.7 .&. C=.+.|
000024C0: 32 22 3A 99 00 CE 2C 49 2A 8D 38 35 31 30 00 05 |2":...,I*.8510..|
000024D0: 2D 4E 2A 99 22 9F 33 9A 20 28 33 58 9B 2D 31 9A |-N*.".3. (3X.-1.|
000024E0: 29 28 58 9B 2D 32 9A 29 20 53 49 4E 43 45 20 43 |)(X.-2.) SINCE C|
000024F0: 3D 50 51 3D 28 2D 31 29 28 2D 32 29 3D 32 20 41 |=PQ=(-1)(-2)=2 A|
00002500: 4E 44 22 3A 99 00 38 2D 58 2A 99 22 20 20 20 20 |ND":..8-X*." |
00002510: 20 20 20 20 20 20 20 20 20 20 20 20 20 42 3D 41 | B=A|
00002520: 51 2B 50 3D 28 33 29 28 2D 32 29 2B 28 2D 31 29 |Q+P=(3)(-2)+(-1)|
00002530: 3D 2D 37 22 3A 99 3A 99 00 42 2D 5D 2A 8D 38 35 |=-7":.:..B-]*.85|
00002540: 31 30 00 6E 2D 62 2A 99 22 20 4E 4F 57 20 59 4F |10.n-b*." NOW YO|
00002550: 55 20 54 52 59 2C 20 46 41 43 54 4F 52 49 53 45 |U TRY, FACTORISE|
00002560: 20 33 58 91 32 11 2D 37 58 2B 34 22 3A 99 00 95 | 3X.2.-7X+4":...|
00002570: 2D 6C 2A 97 31 39 38 2C 30 3A 85 20 22 20 12 28 |-l*.198,0:. " .(|
00002580: D2 D2 D2 D2 29 28 D2 D2 D2 29 22 3B 42 31 24 3A |....)(...)";B1$:|
00002590: 99 22 92 93 22 00 D0 2D 76 2A 43 31 24 B2 22 28 |.".."..-v*C1$."(|
000025A0: 33 58 2D 34 29 28 58 2D 31 29 22 3A 43 32 24 B2 |3X-4)(X-1)":C2$.|
000025B0: 22 33 58 91 32 11 2D 33 58 2D 34 58 2B 34 22 3A |"3X.2.-3X-4X+4":|
000025C0: 43 33 24 B2 22 33 58 91 32 11 2D 37 58 2B 34 22 |C3$."3X.2.-7X+4"|
000025D0: 00 F5 2D 80 2A 8B 42 31 24 B2 43 31 24 B0 42 31 |..-.*.B1$.C1$.B1|
000025E0: 24 B2 22 28 58 2D 31 29 28 33 58 2D 34 29 22 89 |$."(X-1)(3X-4)".|
000025F0: 31 30 39 30 30 00 04 2E 85 2A 8B 52 B2 31 89 31 |10900....*.R.1.1|
00002600: 30 38 39 30 00 0E 2E 87 2A 8D 39 31 30 30 00 1D |0890....*.9100..|
00002610: 2E 88 2A 52 B2 31 3A 89 31 30 38 35 30 00 28 2E |..*R.1:.10850.(.|
00002620: 8A 2A 89 31 30 37 35 30 00 32 2E 94 2A 8D 39 30 |.*.10750.2..*.90|
00002630: 30 30 00 5E 2E 9E 2A 99 22 20 9F 45 58 41 4D 50 |00.^..*." .EXAMP|
00002640: 4C 45 20 33 3A 9A 20 46 41 43 54 4F 52 49 53 45 |LE 3:. FACTORISE|
00002650: 20 33 58 91 32 11 2B 35 58 2D 32 22 3A 99 00 74 | 3X.2.+5X-2":..t|
00002660: 2E A8 2A 99 22 20 9F 53 4F 4C 55 54 49 4F 4E 3A |..*." .SOLUTION:|
00002670: 9A 22 3A 99 00 A7 2E B2 2A 99 22 9F 31 9A 20 28 |.":.....*.".1. (|
00002680: 33 58 20 20 29 28 58 20 20 29 20 53 49 4E 43 45 |3X )(X ) SINCE|
00002690: 20 41 20 49 53 20 41 20 50 52 49 4D 45 20 4E 55 | A IS A PRIME NU|
000026A0: 4D 42 45 52 22 3A 99 00 B1 2E B7 2A 8D 38 35 31 |MBER":.....*.851|
000026B0: 30 00 E3 2E BC 2A 99 22 9F 32 9A 20 28 33 58 9B |0....*.".2. (3X.|
000026C0: 2B 11 9D A3 91 9A 20 29 28 58 9B 2B 91 9D A4 11 |+..... )(X.+....|
000026D0: 9A 20 29 20 53 49 4E 43 45 20 43 3D 9B 2D 9A 32 |. ) SINCE C=.-.2|
000026E0: 22 3A 99 00 ED 2E C1 2A 8D 38 35 31 30 00 24 2F |":.....*.8510.$/|
000026F0: C6 2A 99 22 9F 33 9A 20 28 33 58 9B 2D 31 9A 29 |.*.".3. (3X.-1.)|
00002700: 28 58 9B 2B 32 9A 29 20 53 49 4E 43 45 20 43 3D |(X.+2.) SINCE C=|
00002710: 50 51 3D 28 2D 31 29 28 32 29 3D 2D 32 20 41 4E |PQ=(-1)(2)=-2 AN|
00002720: 44 22 3A 99 00 57 2F D0 2A 99 22 20 20 20 20 20 |D":..W/.*." |
00002730: 20 20 20 20 20 20 20 20 20 20 20 20 20 20 42 3D | B=|
00002740: 41 51 2B 50 3D 28 33 29 28 32 29 2B 28 2D 31 29 |AQ+P=(3)(2)+(-1)|
00002750: 3D 35 22 3A 99 3A 99 00 61 2F D5 2A 8D 38 35 31 |=5":.:..a/.*.851|
00002760: 30 00 8D 2F DA 2A 99 22 20 4E 4F 57 20 59 4F 55 |0../.*." NOW YOU|
00002770: 20 54 52 59 2C 20 46 41 43 54 4F 52 49 53 45 3A | TRY, FACTORISE:|
00002780: 20 33 58 91 32 11 2B 58 2D 34 22 3A 99 00 B4 2F | 3X.2.+X-4":.../|
00002790: E4 2A 97 31 39 38 2C 30 3A 85 20 22 20 12 28 D2 |.*.198,0:. " .(.|
000027A0: D2 D2 D2 29 28 D2 D2 D2 29 22 3B 42 31 24 3A 99 |...)(...)";B1$:.|
000027B0: 22 92 93 22 00 EE 2F EE 2A 43 31 24 B2 22 28 33 |".."../.*C1$."(3|
000027C0: 58 2B 34 29 28 58 2D 31 29 22 3A 43 32 24 B2 22 |X+4)(X-1)":C2$."|
000027D0: 33 58 91 32 11 2D 33 58 2B 34 58 2D 34 22 3A 43 |3X.2.-3X+4X-4":C|
000027E0: 33 24 B2 22 33 58 91 32 11 2B 58 2D 34 22 00 13 |3$."3X.2.+X-4"..|
000027F0: 30 F8 2A 8B 42 31 24 B2 43 31 24 B0 42 31 24 B2 |0.*.B1$.C1$.B1$.|
00002800: 22 28 58 2D 31 29 28 33 58 2B 34 29 22 89 31 31 |"(X-1)(3X+4)".11|
00002810: 30 32 30 00 22 30 FD 2A 8B 52 B2 31 89 31 30 37 |020."0.*.R.1.107|
00002820: 35 30 00 2C 30 02 2B 8D 39 31 30 30 00 3B 30 07 |50.,0.+.9100.;0.|
00002830: 2B 52 B2 31 3A 89 31 30 39 37 30 00 45 30 0C 2B |+R.1:.10970.E0.+|
00002840: 8D 39 30 36 30 00 76 30 16 2B 99 22 20 49 4E 20 |.9060.v0.+." IN |
00002850: 4F 55 52 20 45 58 41 4D 50 4C 45 53 20 53 4F 20 |OUR EXAMPLES SO |
00002860: 46 41 52 2C 20 4F 4E 45 20 46 41 43 54 4F 52 20 |FAR, ONE FACTOR |
00002870: 48 41 53 22 3A 99 00 B0 30 20 2B 99 22 20 42 45 |HAS":...0 +." BE|
00002880: 45 4E 20 28 58 2B 11 9D A3 91 9B 31 9A 29 20 4F |EN (X+.....1.) O|
00002890: 52 20 28 41 58 2B 11 9D A3 91 9B 31 9A 29 2E 20 |R (AX+.....1.). |
000028A0: 4C 45 54 27 53 20 4C 4F 4F 4B 20 41 54 22 3A 99 |LET'S LOOK AT":.|
000028B0: 00 DF 30 2A 2B 99 22 20 4F 4E 45 20 57 48 45 52 |..0*+." ONE WHER|
000028C0: 45 20 54 48 49 53 20 49 53 20 4E 4F 54 20 54 48 |E THIS IS NOT TH|
000028D0: 45 20 43 41 53 45 2E 20 9B 41 4C 4C 22 3A 99 00 |E CASE. .ALL":..|
000028E0: 05 31 34 2B 99 22 20 54 48 45 20 53 41 4D 45 20 |.14+." THE SAME |
000028F0: 50 52 49 4E 43 49 50 4C 45 53 20 41 50 50 4C 59 |PRINCIPLES APPLY|
00002900: 2E 9A 22 3A 99 00 32 31 3E 2B 99 22 20 9F 45 58 |..":..21>+." .EX|
00002910: 41 4D 50 4C 45 20 34 3A 9A 20 46 41 43 54 4F 52 |AMPLE 4:. FACTOR|
00002920: 49 53 45 20 33 58 91 32 11 2B 31 30 58 2B 38 22 |ISE 3X.2.+10X+8"|
00002930: 3A 99 00 48 31 48 2B 99 22 20 9F 53 4F 4C 55 54 |:..H1H+." .SOLUT|
00002940: 49 4F 4E 3A 9A 22 3A 99 00 72 31 52 2B 99 22 9F |ION:.":..r1R+.".|
00002950: 31 9A 20 28 33 58 20 20 29 28 58 20 20 29 20 53 |1. (3X )(X ) S|
00002960: 49 4E 43 45 20 41 20 49 53 20 50 52 49 4D 45 22 |INCE A IS PRIME"|
00002970: 3A 99 00 82 31 57 2B 81 4C B2 31 A4 38 30 30 30 |:...1W+.L.1.8000|
00002980: 3A 82 00 B6 31 5C 2B 99 22 9F 32 9A 20 28 33 58 |:...1\+.".2. (3X|
00002990: 9B 2B 9A 20 29 28 58 9B 2B 9A 20 29 20 53 49 4E |.+. )(X.+. ) SIN|
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000047B0: 20 54 48 45 22 3A 99 00 E5 4F 32 32 99 22 20 4E | THE":...O22." N|
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000047D0: 53 20 49 53 20 49 4D 50 4F 52 54 41 4E 54 20 41 |S IS IMPORTANT A|
000047E0: 4E 44 22 3A 99 00 0C 50 37 32 99 22 20 4D 55 53 |ND":...P72." MUS|
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00004800: 41 4D 50 4C 45 3A 9A 22 3A 99 3A 99 00 2B 50 3C |AMPLE:.":.:..+P<|
00004810: 32 99 22 20 46 41 43 54 4F 52 49 53 45 20 41 91 |2." FACTORISE A.|
00004820: 33 11 2B 42 91 33 11 3A 22 3A 99 00 60 50 46 32 |3.+B.3.:":..`PF2|
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000048A0: 29 28 58 5E D2 D2 D2 D2 D2 D2 D2 D2 29 22 3B 42 |)(X^........)";B|
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000048E0: 24 89 31 32 39 34 30 00 04 51 78 32 99 22 20 4E |$.12940..Qx2." N|
000048F0: 4F 54 20 22 42 31 24 22 20 49 20 57 41 4E 54 45 |OT "B1$" I WANTE|
00004900: 44 22 3A 99 00 2D 51 82 32 99 22 20 12 22 43 31 |D":..-Q.2." ."C1|
00004910: 24 22 92 20 52 45 4D 45 4D 42 45 52 20 22 41 31 |$". REMEMBER "A1|
00004920: 24 22 2C 22 3A 99 3A 89 31 32 37 35 30 00 37 51 |$",":.:.12750.7Q|
00004930: 8C 32 8D 39 30 30 30 00 72 51 96 32 99 22 20 53 |.2.9000.rQ.2." S|
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000049D0: 91 32 11 9B 2D 9A 41 91 32 11 42 9B 2D 9A 41 42 |.2..-.A.2.B.-.AB|
000049E0: 91 32 11 9B 2D 9A 42 91 33 11 22 3A 99 3A 99 00 |.2..-.B.3.":.:..|
000049F0: 34 52 B4 32 99 22 20 3D 41 91 33 11 9B 2B 9A 41 |4R.2." =A.3..+.A|
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00004A50: 53 45 20 58 91 33 11 2D 59 91 33 11 22 3A 99 00 |SE X.3.-Y.3.":..|
00004A60: 8D 52 C8 32 97 20 31 39 38 2C 30 3A 85 20 22 20 |.R.2. 198,0:. " |
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00004AC0: 39 32 30 00 CD 52 E6 32 8D 39 30 30 30 00 F7 52 |920..R.2.9000..R|
00004AD0: F0 32 99 22 20 9F 45 58 41 4D 50 4C 45 20 31 3A |.2." .EXAMPLE 1:|
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00004B00: 53 4F 4C 55 54 49 4F 4E 3A 9A 20 49 4E 20 54 48 |SOLUTION:. IN TH|
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00004B20: 91 33 11 20 3D 22 3A 99 3A 99 00 5A 53 04 33 99 |.3. =":.:..ZS.3.|
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00004B50: 2C 20 53 4F 3A 22 3A 99 3A 99 00 8D 53 0E 33 99 |, SO:":.:...S.3.|
00004B60: 22 20 58 91 33 11 2B 38 3D 58 91 33 11 2B 32 91 |" X.3.+8=X.3.+2.|
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00004B90: 18 33 99 22 20 20 20 20 20 20 20 20 20 20 20 3D |.3." =|
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00004BB0: 22 3A 99 3A 99 00 EA 53 22 33 99 22 20 4E 4F 57 |":.:...S"3." NOW|
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00004BD0: 49 53 45 20 59 91 33 11 2B 32 37 20 9B 28 55 53 |ISE Y.3.+27 .(US|
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00004BF0: 22 20 46 4F 52 20 59 91 32 11 29 9A 22 3A 99 00 |" FOR Y.2.).":..|
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00004C50: 31 34 30 00 74 54 41 33 8B 42 31 24 B2 22 28 59 |140.tTA3.B1$."(Y|
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00004CA0: 33 8D 39 30 36 30 00 D6 54 5E 33 99 22 20 9F 45 |3.9060..T^3." .E|
00004CB0: 58 41 4D 50 4C 45 20 32 3A 9A 20 46 41 43 54 4F |XAMPLE 2:. FACTO|
00004CC0: 52 49 53 45 20 32 37 58 91 33 11 2D 38 59 91 33 |RISE 27X.3.-8Y.3|
00004CD0: 11 22 3A 99 3A 99 00 0E 55 68 33 99 22 20 9F 53 |.":.:...Uh3." .S|
00004CE0: 4F 4C 55 54 49 4F 4E 3A 9A 20 49 4E 20 54 48 45 |OLUTION:. IN THE|
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00004D00: 33 11 20 41 3D 33 58 20 26 22 3A 99 3A 99 00 41 |3. A=3X &":.:..A|
00004D10: 55 72 33 99 22 20 42 3D 33 59 20 53 4F 20 32 37 |Ur3." B=3Y SO 27|
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00004D30: 33 11 2D 28 32 59 29 91 33 11 20 3D 22 3A 99 3A |3.-(2Y).3. =":.:|
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00004DB0: 22 20 46 41 43 54 4F 52 49 53 45 20 38 58 91 33 |" FACTORISE 8X.3|
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00004E30: 42 31 24 B2 43 31 24 B0 42 31 24 B2 22 28 32 58 |B1$.C1$.B1$."(2X|
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00004E60: 31 89 31 32 39 32 30 00 71 56 B2 33 8D 39 31 30 |1.12920.qV.3.910|
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00004E90: 33 99 22 20 49 54 20 4C 4F 4F 4B 53 20 4C 49 4B |3." IT LOOKS LIK|
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00004ED0: 57 45 27 4C 4C 20 4A 55 53 54 20 4D 41 4B 45 20 |WE'LL JUST MAKE |
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00004EF0: 49 54 48 20 41 20 53 48 4F 52 54 20 51 55 49 5A |ITH A SHORT QUIZ|
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00004F10: 45 20 57 49 54 48 22 3A 99 00 49 57 E0 33 99 22 |E WITH":..IW.3."|
00004F20: 20 45 41 43 48 20 51 55 45 53 54 49 4F 4E 20 41 | EACH QUESTION A|
00004F30: 4E 44 20 54 59 50 45 20 41 4C 4C 20 41 4E 53 57 |ND TYPE ALL ANSW|
00004F40: 45 52 53 20 49 4E 22 3A 99 00 7B 57 EA 33 99 22 |ERS IN":..{W.3."|
00004F50: 20 54 48 45 20 46 4F 52 4D 41 54 20 53 48 4F 57 | THE FORMAT SHOW|
00004F60: 4E 20 49 4E 20 54 48 45 20 51 55 45 53 54 49 4F |N IN THE QUESTIO|
00004F70: 4E 2C 20 49 2E 45 2E 9A 22 3A 99 00 A0 57 F4 33 |N, I.E..":...W.3|
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00004FA0: 00 AA 57 FE 33 8D 39 33 30 30 00 B0 57 08 34 8E |..W.3.9300..W.4.|
00004FB0: 00 E2 57 B0 36 99 22 20 41 4E 20 12 41 4C 47 45 |..W.6." AN .ALGE|
00004FC0: 42 52 41 49 43 20 46 52 41 43 54 49 4F 4E 92 20 |BRAIC FRACTION. |
00004FD0: 49 53 20 53 49 4D 50 4C 59 20 41 20 46 52 41 43 |IS SIMPLY A FRAC|
00004FE0: 2D 22 00 15 58 BA 36 99 22 20 54 49 4F 4E 20 57 |-"..X.6." TION W|
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00005000: 52 9A 20 49 53 20 41 4E 20 41 4C 47 45 42 52 41 |R. IS AN ALGEBRA|
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00005020: 52 45 53 53 49 4F 4E 2E 20 4E 4F 57 20 59 4F 55 |RESSION. NOW YOU|
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00005040: 54 49 4F 4E 22 00 76 58 C4 36 99 22 20 49 4E 20 |TION".vX.6." IN |
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00005090: 53 20 52 45 46 45 52 52 45 44 20 54 4F 20 41 53 |S REFERRED TO AS|
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000050E0: 45 42 52 41 49 43 20 46 52 41 43 54 49 4F 4E 22 |EBRAIC FRACTION"|
000050F0: 3A 8B 42 31 24 B2 43 31 24 89 31 34 30 38 30 00 |:.B1$.C1$.14080.|
00005100: 22 59 EC 36 99 22 20 4E 4F 20 22 42 31 24 22 20 |"Y.6." NO "B1$" |
00005110: 49 53 20 4E 4F 54 20 43 4F 52 52 45 43 54 2E 22 |IS NOT CORRECT."|
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00005130: 92 20 49 53 20 43 4F 52 52 45 43 54 20 53 49 4E |. IS CORRECT SIN|
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000051A0: 45 42 52 41 49 43 20 45 58 50 52 45 53 53 49 4F |EBRAIC EXPRESSIO|
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000051D0: 54 4F 52 9A 2E 20 28 58 2B 32 29 2F 33 20 49 53 |TOR.. (X+2)/3 IS|
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000051F0: 49 4E 43 45 20 54 48 45 20 44 45 4E 4F 4D 49 4E |INCE THE DENOMIN|
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00005210: 9A 20 41 4E 22 3A 99 00 46 5A 32 37 99 22 20 41 |. AN":..FZ27." A|
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00005230: 49 4F 4E 2E 20 49 53 20 33 2F 28 58 91 32 11 29 |ION. IS 3/(X.2.)|
00005240: 20 41 4E 22 3A 99 00 82 5A 3C 37 97 31 39 38 2C | AN":...Z<7.198,|
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00005260: 46 52 41 43 54 49 4F 4E 20 28 59 45 53 20 4F 52 |FRACTION (YES OR|
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00005280: 92 22 00 97 5A 46 37 8B 42 31 24 B2 22 59 45 53 |."..ZF7.B1$."YES|
00005290: 22 89 31 34 31 37 30 00 D2 5A 50 37 99 22 93 22 |".14170..ZP7."."|
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000052B0: 9A 20 41 4E 20 41 4C 47 45 42 52 41 49 43 20 46 |. AN ALGEBRAIC F|
000052C0: 52 41 43 54 49 4F 4E 21 22 3A 99 3A 89 31 34 30 |RACTION!":.:.140|
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000052E0: 37 99 22 20 49 53 20 28 58 91 32 11 2B 59 91 32 |7." IS (X.2.+Y.2|
000052F0: 11 29 2F 32 20 41 4E 20 41 4C 47 45 42 52 41 49 |.)/2 AN ALGEBRAI|
00005300: 43 20 46 52 41 43 54 49 4F 4E 22 3A 99 00 37 5B |C FRACTION":..7[|
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00005330: 24 3A 99 22 92 93 22 00 4B 5B 78 37 8B 42 31 24 |$:."..".K[x7.B1$|
00005340: B2 22 4E 4F 22 89 31 34 32 32 30 00 7C 5B 82 37 |."NO".14220.|[.7|
00005350: 99 22 20 4E 4F 20 49 54 20 49 53 20 9B 4E 4F 54 |." NO IT IS .NOT|
00005360: 9A 2C 20 54 48 45 20 44 45 4E 4F 4D 49 4E 41 54 |., THE DENOMINAT|
00005370: 4F 52 20 28 32 29 20 49 53 22 3A 99 00 AC 5B 87 |OR (2) IS":...[.|
00005380: 37 99 22 20 9B 4E 4F 54 9A 20 41 4E 20 41 4C 47 |7." .NOT. AN ALG|
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000053A0: 4E 2E 22 3A 99 3A 89 31 34 30 30 30 00 B6 5B 8C |N.":.:.14000..[.|
000053B0: 37 8D 39 30 30 30 00 E8 5B 96 37 99 22 20 9B 54 |7.9000..[.7." .T|
000053C0: 48 45 20 53 41 4D 45 20 4C 41 57 53 20 41 50 50 |HE SAME LAWS APP|
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000053F0: 54 49 4F 4E 53 20 41 53 20 54 48 45 59 20 44 4F |TIONS AS THEY DO|
00005400: 20 54 4F 20 41 52 49 54 48 4D 45 54 49 43 20 46 | TO ARITHMETIC F|
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00005420: 29 22 9A 32 34 20 20 20 28 31 32 29 28 32 29 20 |)".24 (12)(2) |
00005430: 20 20 31 32 22 00 65 5C AA 37 99 22 20 9B 54 49 | 12".e\.7." .TI|
00005440: 4F 4E 53 2E 9A 20 45 2E 47 2E 20 C0 C0 20 3D 20 |ONS.. E.G. .. = |
00005450: C0 C0 C0 C0 C0 C0 C0 20 3D 20 C0 C0 D6 32 3D 31 |....... = ...2=1|
00005460: D6 32 3D 32 22 00 84 5C AC 37 99 A6 31 33 29 22 |.2=2"..\.7..13)"|
00005470: 31 32 20 20 20 28 31 32 29 20 20 20 20 20 20 31 |12 (12) 1|
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00005490: 49 53 20 41 20 43 4F 4D 4D 4F 4E 20 46 41 43 54 |IS A COMMON FACT|
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000054C0: 32 29 28 58 29 20 20 20 58 22 00 F8 5C BE 37 99 |2)(X) X"..\.7.|
000054D0: 22 20 C0 C0 20 3D 20 C0 C0 C0 C0 C0 C0 20 3D 20 |" .. = ...... = |
000054E0: C0 20 D6 20 32 20 3D 20 31 D6 32 3D 32 2E 20 9B |. . 2 = 1.2=2. .|
000054F0: 58 20 49 53 20 41 9A 22 00 12 5D C0 37 99 22 20 |X IS A."..].7." |
00005500: 58 20 20 20 20 20 20 20 28 58 29 20 20 20 58 22 |X (X) X"|
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00005520: 4E 20 46 41 43 54 4F 52 2E 9A 20 53 4F 20 54 4F |N FACTOR.. SO TO|
00005530: 20 9F 53 49 4D 50 4C 49 46 59 9A 20 41 4C 47 45 | .SIMPLIFY. ALGE|
00005540: 42 52 41 49 43 22 00 77 5D D2 37 99 22 20 46 52 |BRAIC".w].7." FR|
00005550: 41 43 54 49 4F 4E 53 20 57 45 20 4C 4F 4F 4B 20 |ACTIONS WE LOOK |
00005560: 46 4F 52 20 9B 43 4F 4D 4D 4F 4E 20 46 41 43 54 |FOR .COMMON FACT|
00005570: 4F 52 53 9A 22 3A 99 00 A8 5D DC 37 99 22 20 49 |ORS.":...].7." I|
00005580: 4E 20 54 48 45 20 4E 55 4D 45 52 41 54 4F 52 20 |N THE NUMERATOR |
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000055D0: 4D 4D 4F 4E 22 3A 99 00 00 5E EB 37 97 31 39 38 |MMON":...^.7.198|
000055E0: 2C 30 3A 85 20 22 20 46 41 43 54 4F 52 20 49 53 |,0:. " FACTOR IS|
000055F0: 20 12 D2 D2 D2 22 3B 42 31 24 3A 99 22 92 93 22 | ....";B1$:.".."|
00005600: 00 29 5E F0 37 43 31 24 B2 22 58 2B 32 22 3A 8B |.)^.7C1$."X+2":.|
00005610: 42 31 24 B2 43 31 24 B0 42 31 24 B2 22 28 58 2B |B1$.C1$.B1$."(X+|
00005620: 32 29 22 89 31 34 33 34 30 00 54 5E FA 37 99 22 |2)".14340.T^.7."|
00005630: 20 4E 4F 2C 20 4E 4F 54 20 22 42 31 24 22 2E 20 | NO, NOT "B1$". |
00005640: 12 22 43 31 24 22 92 20 49 53 20 52 49 47 48 54 |."C1$". IS RIGHT|
00005650: 2E 22 3A 99 00 6B 5E FF 37 81 4C B2 31 A4 31 35 |.":..k^.7.L.1.15|
00005660: 30 30 3A 82 3A 89 31 34 32 33 30 00 75 5E 04 38 |00:.:.14230.u^.8|
00005670: 8D 39 30 30 30 00 A6 5E 0E 38 99 22 20 41 4E 44 |.9000..^.8." AND|
00005680: 20 28 58 2B 32 29 2F 28 58 2B 32 29 20 3D 20 31 | (X+2)/(X+2) = 1|
00005690: 2C 20 53 4F 20 5B 58 28 58 2B 32 29 5D 2F 28 58 |, SO [X(X+2)]/(X|
000056A0: 2B 32 29 22 3A 99 00 D5 5E 18 38 99 22 20 3D 20 |+2)":...^.8." = |
000056B0: 28 58 29 28 31 29 3D 58 2E 20 4E 4F 57 20 59 4F |(X)(1)=X. NOW YO|
000056C0: 55 20 54 52 59 2C 20 53 49 4D 50 4C 49 46 59 3A |U TRY, SIMPLIFY:|
000056D0: 22 3A 99 3A 99 00 08 5F 22 38 97 31 39 38 2C 30 |":.:..._"8.198,0|
000056E0: 3A 85 20 22 20 5B 58 28 58 91 32 11 2D 33 58 29 |:. " [X(X.2.-3X)|
000056F0: 5D 2F 28 58 91 32 11 2D 33 58 29 20 12 D2 22 3B |]/(X.2.-3X) ..";|
00005700: 42 31 24 3A 99 22 92 22 00 23 5F 2C 38 43 31 24 |B1$:.".".#_,8C1$|
00005710: B2 22 58 22 3A 8B 42 31 24 B2 43 31 24 89 31 34 |."X":.B1$.C1$.14|
00005720: 34 30 30 00 33 5F 36 38 99 22 93 22 3A 89 31 34 |400.3_68.".":.14|
00005730: 33 33 30 00 3D 5F 40 38 8D 39 30 30 30 00 69 5F |330.=_@8.9000.i_|
00005740: 4A 38 99 22 20 4F 46 20 43 4F 55 52 53 45 20 54 |J8." OF COURSE T|
00005750: 48 45 20 45 58 50 52 45 53 53 49 4F 4E 53 20 41 |HE EXPRESSIONS A|
00005760: 52 45 20 4E 4F 54 22 3A 99 00 99 5F 54 38 99 22 |RE NOT":..._T8."|
00005770: 20 55 53 55 41 4C 4C 59 20 53 4F 20 4F 42 56 49 | USUALLY SO OBVI|
00005780: 4F 55 53 20 26 20 4D 55 53 54 20 4E 4F 52 4D 41 |OUS & MUST NORMA|
00005790: 4C 4C 59 20 42 45 22 3A 99 00 CB 5F 5E 38 99 22 |LLY BE":..._^8."|
000057A0: 20 12 46 41 43 54 4F 52 49 53 45 44 92 2E 20 53 | .FACTORISED.. S|
000057B0: 4F 20 54 4F 20 53 49 4D 50 4C 49 46 59 20 41 4E |O TO SIMPLIFY AN|
000057C0: 20 41 4C 47 45 42 52 41 49 43 22 00 FA 5F 68 38 | ALGEBRAIC".._h8|
000057D0: 99 22 20 46 52 41 43 54 49 4F 4E 2C 20 49 54 20 |." FRACTION, IT |
000057E0: 55 53 55 41 4C 4C 59 20 48 41 53 20 54 4F 20 46 |USUALLY HAS TO F|
000057F0: 49 52 53 54 20 42 45 22 3A 99 00 20 60 72 38 97 |IRST BE":.. `r8.|
00005800: 31 39 38 2C 30 3A 85 20 22 20 12 D2 D2 D2 D2 D2 |198,0:. " ......|
00005810: D2 D2 D2 D2 D2 22 3B 42 31 24 3A 99 22 92 93 22 |.....";B1$:.".."|
00005820: 00 44 60 7C 38 43 31 24 B2 22 46 41 43 54 4F 52 |.D`|8C1$."FACTOR|
00005830: 49 53 45 44 22 3A 8B 42 31 24 B2 43 31 24 89 31 |ISED":.B1$.C1$.1|
00005840: 34 34 38 30 00 75 60 86 38 99 22 20 4E 4F 54 20 |4480.u`.8." NOT |
00005850: 22 42 31 24 22 20 54 48 45 20 43 4F 52 52 45 43 |"B1$" THE CORREC|
00005860: 54 20 41 4E 53 57 45 52 20 49 53 22 3A 99 3A 89 |T ANSWER IS":.:.|
00005870: 31 34 34 33 30 00 7F 60 90 38 8D 39 30 30 30 00 |14430..`.8.9000.|
00005880: B2 60 9A 38 99 22 20 9F 45 58 41 4D 50 4C 45 3A |.`.8." .EXAMPLE:|
00005890: 9A 20 53 49 4D 50 4C 49 46 59 20 28 33 58 91 32 |. SIMPLIFY (3X.2|
000058A0: 11 2D 37 58 2D 36 29 2F 28 58 2D 33 29 22 3A 99 |.-7X-6)/(X-3)":.|
000058B0: 3A 99 00 DD 60 A4 38 99 22 20 9F 53 4F 4C 55 54 |:...`.8." .SOLUT|
000058C0: 49 4F 4E 3A 9A 20 28 33 58 91 32 11 2D 37 58 2D |ION:. (3X.2.-7X-|
000058D0: 36 29 2F 28 58 2D 33 29 20 3D 22 3A 99 00 0E 61 |6)/(X-3) =":...a|
000058E0: AE 38 99 22 9F 31 9A 20 5B 28 33 58 2B 32 29 28 |.8.".1. [(3X+2)(|
000058F0: 58 2D 33 29 5D 2F 28 58 2D 33 29 3D 20 20 46 41 |X-3)]/(X-3)= FA|
00005900: 43 54 4F 52 49 53 49 4E 47 22 3A 99 3A 99 00 27 |CTORISING":.:..'|
00005910: 61 B8 38 99 2C 2C 22 20 20 20 20 20 33 58 91 32 |a.8.,," 3X.2|
00005920: 11 2D 37 58 2D 36 22 00 31 61 BD 38 8D 38 35 31 |.-7X-6".1a.8.851|
00005930: 30 00 4D 61 BE 38 99 2C 2C 22 20 20 20 2D 2D 2D |0.Ma.8.,," ---|
00005940: 2D 2D 2D 2D 2D 2D 2D 2D 2D 2D 2D 2D 22 00 6C 61 |------------".la|
00005950: C0 38 99 2C 22 20 58 2D 33 22 2C 22 20 20 20 20 |.8.," X-3"," |
00005960: 20 28 58 2D 33 29 20 49 53 20 41 22 00 85 61 C2 | (X-3) IS A"..a.|
00005970: 38 99 22 9F 32 9A 20 28 33 58 2B 32 29 20 D6 20 |8.".2. (3X+2) . |
00005980: C0 C0 C0 3D 22 00 A9 61 C4 38 99 2C 22 20 58 2D |...="..a.8.," X-|
00005990: 33 22 2C 22 20 20 20 20 20 43 4F 4D 4D 4F 4E 20 |3"," COMMON |
000059A0: 46 41 43 54 4F 52 22 3A 99 00 B3 61 CC 38 8D 38 |FACTOR":...a.8.8|
000059B0: 35 31 30 00 DE 61 D6 38 99 22 9F 33 9A 20 33 58 |510..a.8.".3. 3X|
000059C0: 2B 32 20 53 49 4E 43 45 20 28 58 2D 33 29 2F 28 |+2 SINCE (X-3)/(|
000059D0: 58 2D 33 29 20 3D 20 31 2E 22 3A 99 3A 99 00 E8 |X-3) = 1.":.:...|
000059E0: 61 DB 38 8D 38 35 31 30 00 1B 62 E0 38 99 22 20 |a.8.8510..b.8." |
000059F0: 4E 4F 57 20 59 4F 55 20 54 52 59 2C 20 53 49 4D |NOW YOU TRY, SIM|
00005A00: 50 4C 49 46 59 20 28 32 58 91 32 11 2D 37 58 2B |PLIFY (2X.2.-7X+|
00005A10: 36 29 2F 28 58 2D 32 29 22 3A 99 00 3B 62 EA 38 |6)/(X-2)":..;b.8|
00005A20: 97 31 39 38 2C 30 3A 85 20 22 20 12 D2 D2 D2 D2 |.198,0:. " .....|
00005A30: 22 3B 42 31 24 3A 99 22 92 93 22 00 66 62 F4 38 |";B1$:."..".fb.8|
00005A40: 43 31 24 B2 22 32 58 2D 33 22 3A 8B 42 31 24 B2 |C1$."2X-3":.B1$.|
00005A50: 43 31 24 B0 42 31 24 B2 22 28 32 58 2D 33 29 22 |C1$.B1$."(2X-3)"|
00005A60: 89 31 34 36 33 30 00 75 62 FE 38 8B 52 B2 31 89 |.14630.ub.8.R.1.|
00005A70: 31 34 36 32 30 00 7F 62 08 39 8D 39 31 30 30 00 |14620..b.9.9100.|
00005A80: 8E 62 12 39 52 B2 31 3A 89 31 34 35 36 30 00 99 |.b.9R.1:.14560..|
00005A90: 62 1C 39 89 31 34 33 33 30 00 A3 62 26 39 8D 39 |b.9.14330..b&9.9|
00005AA0: 30 30 30 00 D3 62 30 39 99 22 20 9B 54 4F 20 4D |000..b09." .TO M|
00005AB0: 55 4C 54 49 50 4C 59 20 26 20 44 49 56 49 44 45 |ULTIPLY & DIVIDE|
00005AC0: 20 41 4C 47 45 42 52 41 49 43 20 46 52 41 43 2D | ALGEBRAIC FRAC-|
00005AD0: 22 3A 99 00 03 63 3A 39 99 22 20 54 49 4F 4E 53 |":...c:9." TIONS|
00005AE0: 20 57 45 20 46 41 43 54 4F 52 49 53 45 20 57 48 | WE FACTORISE WH|
00005AF0: 45 52 45 20 50 4F 53 53 49 42 4C 45 20 41 4E 44 |ERE POSSIBLE AND|
00005B00: 22 3A 99 00 34 63 44 39 99 22 20 46 4F 4C 4C 4F |":..4cD9." FOLLO|
00005B10: 57 20 54 48 45 20 55 53 55 41 4C 20 52 55 4C 45 |W THE USUAL RULE|
00005B20: 53 20 4F 46 20 41 52 49 54 48 4D 45 54 49 43 2E |S OF ARITHMETIC.|
00005B30: 9A 22 3A 99 00 4C 63 4C 39 99 A6 31 39 29 22 20 |.":..LcL9..19)" |
00005B40: 32 20 20 20 20 58 91 32 11 2D 34 22 00 75 63 4E |2 X.2.-4".ucN|
00005B50: 39 99 22 20 9F 45 58 41 4D 50 4C 45 3A 9A 20 53 |9." .EXAMPLE:. S|
00005B60: 49 4D 50 4C 49 46 59 20 C0 C0 C0 20 D6 20 C0 C0 |IMPLIFY ... . ..|
00005B70: C0 C0 20 3D 22 00 8C 63 50 39 99 A6 31 39 29 22 |.. ="..cP9..19)"|
00005B80: 58 2B 32 20 20 20 20 34 58 22 3A 99 00 96 63 53 |X+2 4X":...cS|
00005B90: 39 8D 38 35 31 30 00 BB 63 56 39 99 A6 31 31 29 |9.8510..cV9..11)|
00005BA0: 22 32 28 58 91 32 11 2D 34 29 20 20 20 32 9B 28 |"2(X.2.-4) 2.(|
00005BB0: 58 2B 32 29 9A 28 58 2D 32 29 22 00 E6 63 58 39 |X+2).(X-2)"..cX9|
00005BC0: 99 22 20 9F 53 4F 4C 55 54 49 4F 4E 3A 9A 20 C0 |." .SOLUTION:. .|
00005BD0: C0 C0 C0 C0 C0 C0 20 3D 20 C0 C0 C0 C0 C0 C0 C0 |...... = .......|
00005BE0: C0 C0 C0 20 3D 22 00 09 64 5A 39 99 A6 31 31 29 |... ="..dZ9..11)|
00005BF0: 22 34 58 28 58 2B 32 29 20 20 20 20 20 34 58 9B |"4X(X+2) 4X.|
00005C00: 28 58 2B 32 29 9A 22 3A 99 00 13 64 5D 39 8D 38 |(X+2).":...d]9.8|
00005C10: 35 31 30 00 2E 64 60 39 99 A6 31 31 29 22 9B 32 |510..d`9..11)".2|
00005C20: 9A 28 58 2D 32 29 20 20 20 20 58 2D 32 22 00 47 |.(X-2) X-2".G|
00005C30: 64 62 39 99 A6 31 31 29 22 C0 C0 C0 C0 C0 C0 C0 |db9..11)".......|
00005C40: 20 3D 20 C0 C0 C0 22 00 63 64 64 39 99 A6 31 31 | = ...".cdd9..11|
00005C50: 29 22 9B 32 9A 28 32 29 28 58 29 20 20 20 32 58 |)".2.(2)(X) 2X|
00005C60: 22 3A 99 00 6D 64 67 39 8D 38 35 31 30 00 8B 64 |":..mdg9.8510..d|
00005C70: 6A 39 99 A6 32 33 29 22 32 58 2B 31 20 20 20 31 |j9..23)"2X+1 1|
00005C80: 32 58 91 32 11 59 2D 36 58 59 22 00 BC 64 6C 39 |2X.2.Y-6XY"..dl9|
00005C90: 99 22 20 4E 4F 57 20 59 4F 55 20 54 52 59 2C 20 |." NOW YOU TRY, |
00005CA0: 53 49 4D 50 4C 49 46 59 20 C0 C0 C0 C0 20 D6 20 |SIMPLIFY .... . |
00005CB0: C0 C0 C0 C0 C0 C0 C0 C0 C0 22 3A 99 00 DB 64 6E |.........":...dn|
00005CC0: 39 99 A6 32 33 29 22 20 58 59 20 20 20 20 20 20 |9..23)" XY |
00005CD0: 31 32 58 91 32 11 2D 33 22 3A 99 00 15 65 76 39 |12X.2.-3":...ev9|
00005CE0: 97 31 39 38 2C 30 3A 52 B2 30 3A 85 20 22 20 9B |.198,0:R.0:. " .|
00005CF0: 28 55 53 45 20 50 45 4E 20 26 20 50 41 50 45 52 |(USE PEN & PAPER|
00005D00: 29 9A 20 20 20 20 3D 20 12 D2 22 3B 42 31 24 3A |). = ..";B1$:|
00005D10: 99 22 92 93 22 00 28 65 80 39 8B 42 31 24 B2 22 |."..".(e.9.B1$."|
00005D20: 32 22 89 31 34 37 34 30 00 3B 65 8A 39 5A B2 31 |2".14740.;e.9Z.1|
00005D30: 3A 52 B2 31 3A 89 31 34 37 36 30 00 45 65 94 39 |:R.1:.14760.Ee.9|
00005D40: 8D 39 30 36 30 00 7A 65 99 39 8B 5A B2 31 A7 99 |.9060.ze.9.Z.1..|
00005D50: 22 20 1E 59 4F 55 27 56 45 20 47 4F 54 20 49 54 |" .YOU'VE GOT IT|
00005D60: 20 54 48 49 53 20 54 49 4D 45 21 9A 22 3A 5A B2 | THIS TIME!.":Z.|
00005D70: 30 3A 99 3A 89 31 34 38 37 30 00 9E 65 9B 39 99 |0:.:.14870..e.9.|
00005D80: 22 20 53 4F 20 54 48 45 20 53 54 45 50 53 20 54 |" SO THE STEPS T|
00005D90: 4F 20 54 41 4B 45 20 41 52 45 3A 22 3A 99 00 A9 |O TAKE ARE:":...|
00005DA0: 65 9E 39 89 31 34 37 38 30 00 D8 65 A8 39 99 22 |e.9.14780..e.9."|
00005DB0: 20 4E 4F 20 12 32 92 20 49 53 20 54 48 45 20 43 | NO .2. IS THE C|
00005DC0: 4F 52 52 45 43 54 20 41 4E 53 57 45 52 2E 20 9B |ORRECT ANSWER. .|
00005DD0: 57 52 49 54 45 22 3A 99 00 04 66 B2 39 99 22 20 |WRITE":...f.9." |
00005DE0: 44 4F 57 4E 20 54 48 45 53 45 20 53 54 45 50 53 |DOWN THESE STEPS|
00005DF0: 20 41 53 20 57 45 20 47 4F 20 22 41 31 24 22 2E | AS WE GO "A1$".|
00005E00: 9A 22 3A 99 00 2D 66 BC 39 99 22 9F 31 9A 20 9B |.":..-f.9.".1. .|
00005E10: 46 41 43 54 4F 52 49 53 45 20 57 48 45 52 45 20 |FACTORISE WHERE |
00005E20: 50 4F 53 53 49 42 4C 45 9A 2E 22 3A 99 00 5D 66 |POSSIBLE..":..]f|
00005E30: C4 39 99 22 20 32 58 2B 31 20 31 32 58 91 32 11 |.9." 2X+1 12X.2.|
00005E40: 59 2D 36 58 59 20 20 20 32 58 2B 31 20 20 20 28 |Y-6XY 2X+1 (|
00005E50: 36 29 28 58 59 29 28 32 58 2D 31 29 22 00 8D 66 |6)(XY)(2X-1)"..f|
00005E60: C6 39 99 22 20 C0 C0 C0 C0 D6 C0 C0 C0 C0 C0 C0 |.9." ...........|
00005E70: C0 C0 C0 20 3D 20 C0 C0 C0 C0 20 D6 20 C0 C0 C0 |... = .... . ...|
00005E80: C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 22 3A 99 00 BF 66 |..........":...f|
00005E90: C8 39 99 22 20 20 58 59 20 20 20 20 31 32 58 91 |.9." XY 12X.|
00005EA0: 32 11 2D 33 20 20 20 20 20 58 59 20 20 20 20 33 |2.-3 XY 3|
00005EB0: 28 32 58 2B 31 29 28 32 58 2D 31 29 22 3A 99 00 |(2X+1)(2X-1)":..|
00005EC0: C9 66 CB 39 8D 38 35 31 30 00 FA 66 D0 39 99 22 |.f.9.8510..f.9."|
00005ED0: 9F 32 9A 20 9B 4D 55 4C 54 49 50 4C 59 20 26 20 |.2. .MULTIPLY & |
00005EE0: 4C 4F 4F 4B 20 46 4F 52 20 43 4F 4D 4D 4F 4E 20 |LOOK FOR COMMON |
00005EF0: 46 41 43 54 4F 52 53 22 3A 99 00 20 67 D8 39 99 |FACTORS":.. g.9.|
00005F00: A6 31 36 29 22 20 20 9B 28 32 58 2B 31 29 9A 28 |.16)" .(2X+1).(|
00005F10: 36 29 1E 28 58 59 29 9C 28 32 58 2D 31 29 9A 22 |6).(XY).(2X-1)."|
00005F20: 00 41 67 DA 39 99 A6 31 36 29 22 3D 20 C0 C0 C0 |.Ag.9..16)"= ...|
00005F30: C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 C0 |................|
00005F40: 22 00 69 67 DC 39 99 A6 31 36 29 22 20 20 1E 28 |".ig.9..16)" .(|
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00007AE0: 30 00 0F 83 F6 40 97 31 39 38 2C 30 3A 85 22 20 |0....@.198,0:." |
00007AF0: 53 4F 4C 56 45 20 58 2B 31 32 3D 32 30 2E 20 58 |SOLVE X+12=20. X|
00007B00: 3D 20 12 D2 22 3B 42 31 24 3A 99 22 92 93 22 00 |= ..";B1$:."..".|
00007B10: 2A 83 00 41 43 31 24 B2 22 38 22 3A 8B 42 31 24 |*..AC1$."8":.B1$|
00007B20: B2 43 31 24 89 31 36 36 36 30 00 35 83 0A 41 89 |.C1$.16660.5..A.|
00007B30: 31 36 35 35 30 00 3F 83 14 41 8D 39 30 30 30 00 |16550.?..A.9000.|
00007B40: 73 83 1E 41 99 22 9F 33 9B 20 45 51 55 41 4C 53 |s..A.".3. EQUALS|
00007B50: 20 4D 55 4C 54 49 50 4C 49 45 44 20 42 59 20 45 | MULTIPLIED BY E|
00007B60: 51 55 41 4C 53 20 41 52 45 20 45 51 55 41 4C 9A |QUALS ARE EQUAL.|
00007B70: 22 3A 99 00 80 83 26 41 99 22 20 20 20 20 58 22 |":....&A." X"|
00007B80: 00 B2 83 28 41 99 22 20 20 20 20 C0 20 3D 20 36 |...(A." . = 6|
00007B90: 22 2C 22 20 20 20 20 9B 4D 55 4C 54 49 50 4C 59 |"," .MULTIPLY|
00007BA0: 20 42 4F 54 48 20 53 49 44 45 53 9A 20 42 59 20 | BOTH SIDES. BY |
00007BB0: 35 22 00 C1 83 2A 41 99 22 20 20 20 20 35 22 3A |5"...*A." 5":|
00007BC0: 99 00 CB 83 2D 41 8D 38 35 31 30 00 DD 83 30 41 |....-A.8510...0A|
00007BD0: 99 22 20 20 20 20 58 9B 28 35 29 9A 22 00 0D 84 |." X.(5)."...|
00007BE0: 32 41 99 22 20 53 4F 20 C0 C0 C0 C0 20 3D 20 36 |2A." SO .... = 6|
00007BF0: 9B 28 35 29 9A 20 54 48 55 53 20 58 3D 33 30 2E |.(5). THUS X=30.|
00007C00: 20 4E 4F 57 20 59 4F 55 20 54 52 59 22 00 1D 84 | NOW YOU TRY"...|
00007C10: 34 41 99 22 20 20 20 20 20 35 22 3A 99 00 27 84 |4A." 5":..'.|
00007C20: 37 41 8D 38 35 31 30 00 56 84 3C 41 97 31 39 38 |7A.8510.V.<A.198|
00007C30: 2C 30 3A 85 22 20 53 4F 4C 56 45 20 59 2F 33 20 |,0:." SOLVE Y/3 |
00007C40: 3D 20 34 2E 20 59 3D 20 12 D2 D2 22 3B 42 31 24 |= 4. Y= ...";B1$|
00007C50: 3A 99 22 92 93 22 00 72 84 46 41 43 31 24 B2 22 |:."..".r.FAC1$."|
00007C60: 31 32 22 3A 8B 42 31 24 B2 43 31 24 89 31 36 37 |12":.B1$.C1$.167|
00007C70: 33 30 00 7D 84 50 41 89 31 36 35 35 30 00 87 84 |30.}.PA.16550...|
00007C80: 5A 41 8D 39 30 30 30 00 B7 84 64 41 99 22 9F 34 |ZA.9000...dA.".4|
00007C90: 9B 20 45 51 55 41 4C 53 20 44 49 56 49 44 45 44 |. EQUALS DIVIDED|
00007CA0: 20 42 59 20 45 51 55 41 4C 53 20 41 52 45 20 45 | BY EQUALS ARE E|
00007CB0: 51 55 41 4C 22 3A 99 00 E7 84 6E 41 99 22 9E 20 |QUAL":....nA.". |
00007CC0: 20 53 4F 20 4C 4F 4E 47 20 41 53 20 54 48 45 20 | SO LONG AS THE |
00007CD0: 44 49 56 49 53 4F 52 20 49 53 20 4E 4F 54 20 5A |DIVISOR IS NOT Z|
00007CE0: 45 52 4F 9A 22 3A 99 00 19 85 78 41 99 22 20 20 |ERO.":....xA." |
00007CF0: 20 20 33 58 3D 31 32 20 20 20 20 20 20 20 9B 44 | 3X=12 .D|
00007D00: 49 56 49 44 45 20 42 4F 54 48 20 53 49 44 45 53 |IVIDE BOTH SIDES|
00007D10: 9A 20 42 59 20 33 22 3A 99 00 23 85 82 41 8D 38 |. BY 3":..#..A.8|
00007D20: 35 31 30 00 36 85 8A 41 99 22 20 20 20 20 33 58 |510.6..A." 3X|
00007D30: 20 20 20 31 32 22 00 63 85 8C 41 99 22 20 53 4F | 12".c..A." SO|
00007D40: 20 9B C0 C0 9A 20 3D 20 9B C0 C0 9A 20 54 48 55 | .... = .... THU|
00007D50: 53 20 58 3D 34 2E 20 4E 4F 57 20 59 4F 55 20 54 |S X=4. NOW YOU T|
00007D60: 52 59 22 00 79 85 8E 41 99 22 20 20 20 20 9B 33 |RY".y..A." .3|
00007D70: 20 20 20 20 33 9A 22 3A 99 00 83 85 96 41 8D 38 | 3.":.....A.8|
00007D80: 35 31 30 00 B1 85 A0 41 97 31 39 38 2C 30 3A 85 |510....A.198,0:.|
00007D90: 22 20 53 4F 4C 56 45 20 35 58 3D 31 30 30 2E 20 |" SOLVE 5X=100. |
00007DA0: 58 3D 20 12 D2 D2 22 3B 42 31 24 3A 99 22 92 93 |X= ...";B1$:."..|
00007DB0: 22 00 CD 85 AA 41 43 31 24 B2 22 32 30 22 3A 8B |"....AC1$."20":.|
00007DC0: 42 31 24 B2 43 31 24 89 31 36 38 33 30 00 D8 85 |B1$.C1$.16830...|
00007DD0: B4 41 89 31 36 35 35 30 00 E2 85 BE 41 8D 39 30 |.A.16550....A.90|
00007DE0: 30 30 00 0B 86 C8 41 99 22 9F 35 9B 20 50 4F 57 |00....A.".5. POW|
00007DF0: 45 52 53 20 4F 46 20 45 51 55 41 4C 53 20 41 52 |ERS OF EQUALS AR|
00007E00: 45 20 45 51 55 41 4C 9A 22 3A 99 00 41 86 D2 41 |E EQUAL.":..A..A|
00007E10: 99 22 20 20 20 20 20 AC CE 58 2D 33 91 9D 9D 9D |." ..X-3....|
00007E20: AF AF AF 11 3D 34 22 2C 22 9B 53 51 55 41 52 45 |....=4",".SQUARE|
00007E30: 20 42 4F 54 48 20 53 49 44 45 53 9A 22 3A 99 3A | BOTH SIDES.":.:|
00007E40: 99 00 4B 86 D7 41 8D 38 35 31 30 00 77 86 DC 41 |..K..A.8510.w..A|
00007E50: 99 22 20 53 4F 20 28 AC CE 58 2D 33 91 9D 9D 9D |." SO (..X-3....|
00007E60: AF AF AF 11 29 91 32 11 3D 34 91 32 11 20 48 45 |....).2.=4.2. HE|
00007E70: 4E 43 45 3A 22 3A 99 00 AB 86 E6 41 99 22 20 20 |NCE:":.....A." |
00007E80: 20 20 20 58 2D 33 3D 31 36 20 20 20 20 20 20 20 | X-3=16 |
00007E90: 20 9B 41 44 44 9A 20 33 20 9B 54 4F 20 42 4F 54 | .ADD. 3 .TO BOT|
00007EA0: 48 20 53 49 44 45 53 9A 22 3A 99 00 B5 86 EB 41 |H SIDES.":.....A|
00007EB0: 8D 38 35 31 30 00 EC 86 F0 41 99 22 20 53 4F 20 |.8510....A." SO |
00007EC0: 20 58 3D 31 39 2E 20 4E 4F 57 20 59 4F 55 20 54 | X=19. NOW YOU T|
00007ED0: 52 59 2E 20 53 4F 4C 56 45 20 AC CE 58 2B 32 91 |RY. SOLVE ..X+2.|
00007EE0: 9D 9D 9D AF AF AF 11 3D 32 22 3A 99 00 0B 87 FA |.......=2":.....|
00007EF0: 41 97 31 39 38 2C 30 3A 85 22 20 58 3D 20 12 D2 |A.198,0:." X= ..|
00007F00: 22 3B 42 31 24 3A 99 22 92 93 22 00 26 87 04 42 |";B1$:."..".&..B|
00007F10: 43 31 24 B2 22 32 22 3A 8B 42 31 24 B2 43 31 24 |C1$."2":.B1$.C1$|
00007F20: 89 31 36 39 32 30 00 31 87 0E 42 89 31 36 35 35 |.16920.1..B.1655|
00007F30: 30 00 3B 87 18 42 8D 39 30 30 30 00 6E 87 22 42 |0.;..B.9000.n."B|
00007F40: 99 22 20 41 20 12 46 4F 52 4D 55 4C 41 92 20 49 |." A .FORMULA. I|
00007F50: 53 20 41 4E 20 45 51 55 41 54 49 4F 4E 20 57 48 |S AN EQUATION WH|
00007F60: 49 43 48 20 45 58 50 52 45 53 2D 22 3A 99 00 A0 |ICH EXPRES-":...|
00007F70: 87 2C 42 99 22 20 53 45 53 20 41 20 47 45 4E 45 |.,B." SES A GENE|
00007F80: 52 41 4C 20 52 55 4C 45 20 4F 52 20 4C 41 57 20 |RAL RULE OR LAW |
00007F90: 28 4C 49 4B 45 20 45 3D 4D 43 91 32 11 29 2E 22 |(LIKE E=MC.2.)."|
00007FA0: 00 D1 87 36 42 99 22 20 4E 4F 57 20 59 4F 55 20 |...6B." NOW YOU |
00007FB0: 54 45 4C 4C 20 4D 45 2C 20 41 4E 20 45 51 55 41 |TELL ME, AN EQUA|
00007FC0: 54 49 4F 4E 20 57 48 49 43 48 20 45 58 2D 22 3A |TION WHICH EX-":|
00007FD0: 99 00 FE 87 40 42 99 22 20 50 52 45 53 53 45 53 |....@B." PRESSES|
00007FE0: 20 41 20 47 45 4E 45 52 41 4C 20 52 55 4C 45 20 | A GENERAL RULE |
00007FF0: 4F 52 20 4C 41 57 20 49 53 20 41 22 3A 99 00 20 |OR LAW IS A":.. |
00008000: 88 4A 42 97 31 39 38 2C 30 3A 85 22 20 12 D2 D2 |.JB.198,0:." ...|
00008010: D2 D2 D2 D2 D2 22 3B 42 31 24 3A 99 22 92 93 22 |.....";B1$:.".."|
00008020: 00 41 88 54 42 43 31 24 B2 22 46 4F 52 4D 55 4C |.A.TBC1$."FORMUL|
00008030: 41 22 3A 8B 42 31 24 B2 43 31 24 89 31 37 30 31 |A":.B1$.C1$.1701|
00008040: 30 00 69 88 5E 42 99 22 20 49 27 4D 20 53 4F 52 |0.i.^B." I'M SOR|
00008050: 52 59 20 42 55 54 20 22 42 31 24 22 20 49 53 20 |RY BUT "B1$" IS |
00008060: 57 52 4F 4E 47 2E 22 3A 99 00 95 88 68 42 99 22 |WRONG.":....hB."|
00008070: 20 12 22 43 31 24 22 92 20 49 53 20 43 4F 52 52 | ."C1$". IS CORR|
00008080: 45 43 54 2E 20 41 47 41 49 4E 3A 22 3A 99 3A 89 |ECT. AGAIN:":.:.|
00008090: 31 36 39 33 30 00 9F 88 72 42 8D 39 30 30 30 00 |16930...rB.9000.|
000080A0: CD 88 7C 42 99 22 20 41 20 46 4F 52 4D 55 4C 41 |..|B." A FORMULA|
000080B0: 20 47 45 4E 45 52 41 4C 4C 59 20 48 41 53 20 53 | GENERALLY HAS S|
000080C0: 45 56 45 52 41 4C 20 55 4E 2D 22 3A 99 00 FE 88 |EVERAL UN-":....|
000080D0: 86 42 99 22 20 4B 4E 4F 57 4E 53 20 28 4C 49 4B |.B." KNOWNS (LIK|
000080E0: 45 20 45 2C 4D 20 26 20 43 29 20 57 48 49 43 48 |E E,M & C) WHICH|
000080F0: 20 41 52 45 20 43 41 4C 4C 45 44 22 3A 99 00 2F | ARE CALLED":../|
00008100: 89 90 42 99 22 20 12 56 41 52 49 41 42 4C 45 53 |..B." .VARIABLES|
00008110: 92 2E 20 4F 4B 20 59 4F 55 20 54 45 4C 4C 20 4D |.. OK YOU TELL M|
00008120: 45 2C 20 41 20 46 4F 52 4D 55 4C 41 22 3A 99 00 |E, A FORMULA":..|
00008130: 5D 89 9A 42 99 22 20 55 53 55 41 4C 4C 59 20 48 |]..B." USUALLY H|
00008140: 41 53 20 53 45 56 45 52 41 4C 20 55 4E 4B 4E 4F |AS SEVERAL UNKNO|
00008150: 57 4E 53 20 43 41 4C 4C 45 44 22 3A 99 00 81 89 |WNS CALLED":....|
00008160: A4 42 97 31 39 38 2C 30 3A 85 22 20 12 D2 D2 D2 |.B.198,0:." ....|
00008170: D2 D2 D2 D2 D2 D2 22 3B 42 31 24 3A 99 22 92 93 |......";B1$:."..|
00008180: 22 00 A4 89 AE 42 43 31 24 B2 22 56 41 52 49 41 |"....BC1$."VARIA|
00008190: 42 4C 45 53 22 3A 8B 42 31 24 B2 43 31 24 89 31 |BLES":.B1$.C1$.1|
000081A0: 37 30 39 30 00 AF 89 B8 42 89 31 36 39 39 30 00 |7090....B.16990.|
000081B0: B9 89 C2 42 8D 39 30 30 30 00 EB 89 CC 42 99 22 |...B.9000....B."|
000081C0: 20 53 4F 20 54 48 45 20 9B 56 41 52 49 41 42 4C | SO THE .VARIABL|
000081D0: 45 53 9A 20 49 4E 20 46 3D 28 39 2F 35 29 43 2B |ES. IN F=(9/5)C+|
000081E0: 33 32 20 41 52 45 20 43 22 3A 99 00 1E 8A D6 42 |32 ARE C":.....B|
000081F0: 99 22 20 41 4E 44 20 46 2E 20 54 48 45 20 56 41 |." AND F. THE VA|
00008200: 52 49 41 42 4C 45 53 20 49 4E 20 45 3D 4D 43 91 |RIABLES IN E=MC.|
00008210: 32 11 20 41 52 45 20 4D 2C 20 43 22 3A 99 00 3E |2. ARE M, C":..>|
00008220: 8A E0 42 97 31 39 38 2C 30 3A 85 22 20 41 4E 44 |..B.198,0:." AND|
00008230: 20 12 D2 22 3B 42 31 24 3A 99 22 92 93 22 00 59 | ..";B1$:."..".Y|
00008240: 8A EA 42 43 31 24 B2 22 45 22 3A 8B 42 31 24 B2 |..BC1$."E":.B1$.|
00008250: 22 45 22 89 31 37 31 35 30 00 64 8A F4 42 89 31 |"E".17150.d..B.1|
00008260: 36 39 39 30 00 6E 8A FE 42 8D 39 30 30 30 00 9C |6990.n..B.9000..|
00008270: 8A 08 43 99 22 20 54 4F 20 9B 53 4F 4C 56 45 9A |..C." TO .SOLVE.|
00008280: 20 41 20 46 4F 52 4D 55 4C 41 20 46 4F 52 20 4F | A FORMULA FOR O|
00008290: 4E 45 20 4F 46 20 54 48 45 22 3A 99 00 CD 8A 12 |NE OF THE":.....|
000082A0: 43 99 22 20 56 41 52 49 41 42 4C 45 53 20 59 4F |C." VARIABLES YO|
000082B0: 55 20 9B 54 52 41 4E 53 50 4F 53 45 9A 20 54 48 |U .TRANSPOSE. TH|
000082C0: 45 20 45 51 55 41 54 49 4F 4E 22 3A 99 00 FE 8A |E EQUATION":....|
000082D0: 1C 43 99 22 20 53 4F 20 54 48 41 54 20 54 48 45 |.C." SO THAT THE|
000082E0: 20 56 41 52 49 41 42 4C 45 20 49 4E 20 51 55 45 | VARIABLE IN QUE|
000082F0: 53 54 49 4F 4E 20 49 53 20 4F 4E 22 3A 99 00 30 |STION IS ON":..0|
00008300: 8B 26 43 99 22 20 4F 4E 45 20 53 49 44 45 20 42 |.&C." ONE SIDE B|
00008310: 59 20 49 54 53 45 4C 46 2E 20 46 4F 52 20 45 58 |Y ITSELF. FOR EX|
00008320: 41 4D 50 4C 45 20 9F 53 4F 4C 56 45 9A 22 3A 99 |AMPLE .SOLVE.":.|
00008330: 00 63 8B 30 43 99 22 20 43 3D 32 FF 52 20 46 4F |.c.0C." C=2.R FO|
00008340: 52 20 52 20 20 20 20 9B 44 49 56 49 44 45 20 42 |R R .DIVIDE B|
00008350: 4F 54 48 20 53 49 44 45 53 9A 20 42 59 20 32 FF |OTH SIDES. BY 2.|
00008360: 22 3A 99 00 73 8B 3A 43 81 4C B2 31 A4 36 30 30 |":..s.:C.L.1.600|
00008370: 30 3A 82 00 8B 8B 42 43 99 22 20 43 20 20 20 20 |0:....BC." C |
00008380: 32 FF 52 20 20 20 20 20 20 43 22 00 B8 8B 44 43 |2.R C"...DC|
00008390: 99 22 20 C0 C0 20 3D 20 C0 C0 C0 20 53 4F 20 52 |." .. = ... SO R|
000083A0: 3D C0 C0 2E 20 4E 4F 57 20 59 4F 55 20 54 52 59 |=... NOW YOU TRY|
000083B0: 2C 20 53 4F 4C 56 45 22 00 D3 8B 46 43 99 22 20 |, SOLVE"...FC." |
000083C0: 32 FF 20 20 20 32 FF 20 20 20 20 20 20 20 32 FF |2. 2. 2.|
000083D0: 22 3A 99 00 0C 8C 4E 43 97 31 39 38 2C 30 3A 85 |":....NC.198,0:.|
000083E0: 22 20 45 3D 49 52 20 46 4F 52 20 49 20 28 52 20 |" E=IR FOR I (R |
000083F0: 49 53 20 4E 4F 54 20 30 29 20 49 3D 20 12 D2 2F |IS NOT 0) I= ../|
00008400: D2 22 3B 42 31 24 3A 99 22 92 93 22 00 29 8C 58 |.";B1$:."..".).X|
00008410: 43 43 31 24 B2 22 45 2F 52 22 3A 8B 42 31 24 B2 |CC1$."E/R":.B1$.|
00008420: 43 31 24 89 31 37 32 36 30 00 5F 8C 62 43 99 22 |C1$.17260._.bC."|
00008430: 20 4E 4F 54 20 22 42 31 24 22 20 12 22 43 31 24 | NOT "B1$" ."C1$|
00008440: 22 92 20 49 53 20 52 49 47 48 54 2E 20 9F 52 45 |". IS RIGHT. .RE|
00008450: 56 49 45 57 9A 22 3A 99 3A 89 31 36 33 30 30 00 |VIEW.":.:.16300.|
00008460: 69 8C 6C 43 8D 39 30 30 30 00 9B 8C 76 43 99 22 |i.lC.9000...vC."|
00008470: 20 4F 46 54 45 4E 20 59 4F 55 20 41 52 45 20 9B | OFTEN YOU ARE .|
00008480: 47 49 56 45 4E 20 56 41 4C 55 45 53 9A 20 4F 46 |GIVEN VALUES. OF|
00008490: 20 41 4C 4C 20 54 48 45 22 3A 99 00 CB 8C 80 43 | ALL THE":.....C|
000084A0: 99 22 20 56 41 52 49 41 42 4C 45 53 20 45 58 43 |." VARIABLES EXC|
000084B0: 45 50 54 20 4F 4E 45 20 41 4E 44 20 41 52 45 20 |EPT ONE AND ARE |
000084C0: 41 53 4B 45 44 20 54 4F 22 3A 99 00 FE 8C 8A 43 |ASKED TO":.....C|
000084D0: 99 22 20 9B 46 49 4E 44 20 54 48 45 20 56 41 4C |." .FIND THE VAL|
000084E0: 55 45 9A 20 4F 46 20 54 48 41 54 20 4F 4E 45 2E |UE. OF THAT ONE.|
000084F0: 20 54 4F 20 44 4F 20 54 48 49 53 22 3A 99 00 2E | TO DO THIS":...|
00008500: 8D 94 43 99 22 20 59 4F 55 20 9B 54 52 41 4E 53 |..C." YOU .TRANS|
00008510: 50 4F 53 45 9A 20 54 48 45 20 45 51 55 41 54 49 |POSE. THE EQUATI|
00008520: 4F 4E 20 41 4E 44 20 54 48 45 4E 22 3A 99 00 61 |ON AND THEN":..a|
00008530: 8D 9E 43 99 22 20 12 53 55 42 53 54 49 54 55 54 |..C." .SUBSTITUT|
00008540: 45 92 20 54 48 45 20 56 41 4C 55 45 53 20 4F 46 |E. THE VALUES OF|
00008550: 20 54 48 45 20 56 41 52 49 41 42 4C 45 53 22 3A | THE VARIABLES":|
00008560: 99 00 92 8D A8 43 99 22 20 49 4E 20 54 48 45 20 |.....C." IN THE |
00008570: 46 4F 52 4D 55 4C 41 2E 20 4F 4B 20 53 4F 20 54 |FORMULA. OK SO T|
00008580: 45 4C 4C 20 4D 45 2C 20 54 4F 20 46 49 4E 44 22 |ELL ME, TO FIND"|
00008590: 3A 99 00 C1 8D B2 43 99 22 20 49 20 49 4E 20 45 |:.....C." I IN E|
000085A0: 3D 49 52 20 57 48 45 4E 20 45 3D 32 20 26 20 52 |=IR WHEN E=2 & R|
000085B0: 3D 33 2C 20 59 4F 55 20 54 52 41 4E 53 2D 22 3A |=3, YOU TRANS-":|
000085C0: 99 00 F1 8D BC 43 99 22 20 50 4F 53 45 20 54 48 |.....C." POSE TH|
000085D0: 45 20 45 51 55 41 54 49 4F 4E 20 53 4F 20 54 48 |E EQUATION SO TH|
000085E0: 41 54 20 49 20 49 53 20 4F 4E 20 4F 4E 45 22 3A |AT I IS ON ONE":|
000085F0: 99 00 20 8E C6 43 99 22 20 53 49 44 45 20 42 59 |.. ..C." SIDE BY|
00008600: 20 49 54 53 45 4C 46 20 41 4E 44 20 54 48 45 4E | ITSELF AND THEN|
00008610: 20 D2 D2 D2 D2 D2 D2 D2 D2 D2 D2 D2 D2 22 3A 99 | ............":.|
00008620: 00 3F 8E D0 43 99 22 20 32 20 46 4F 52 20 45 20 |.?..C." 2 FOR E |
00008630: 41 4E 44 20 33 20 46 4F 52 20 52 2E 22 3A 99 00 |AND 3 FOR R.":..|
00008640: 64 8E DA 43 97 31 39 38 2C 30 3A 85 22 20 12 D2 |d..C.198,0:." ..|
00008650: D2 D2 D2 D2 D2 D2 D2 D2 D2 22 3B 42 31 24 3A 99 |.........";B1$:.|
00008660: 22 92 93 22 00 88 8E E4 43 43 31 24 B2 22 53 55 |".."....CC1$."SU|
00008670: 42 53 54 49 54 55 54 45 22 3A 8B 42 31 24 B2 43 |BSTITUTE":.B1$.C|
00008680: 31 24 89 31 37 34 30 30 00 93 8E EE 43 89 31 36 |1$.17400....C.16|
00008690: 39 39 30 00 9D 8E F8 43 8D 39 30 30 30 00 AA 8E |990....C.9000...|
000086A0: 00 44 99 A6 31 32 29 22 39 22 00 D7 8E 02 44 99 |.D..12)"9"....D.|
000086B0: 22 20 9F 45 58 41 4D 50 4C 45 3A 9A 20 46 3D C0 |" .EXAMPLE:. F=.|
000086C0: 43 2B 33 32 2E 20 46 49 4E 44 20 43 20 57 48 45 |C+32. FIND C WHE|
000086D0: 4E 20 46 3D 36 38 22 00 E6 8E 04 44 99 A6 31 32 |N F=68"....D..12|
000086E0: 29 22 35 22 3A 99 00 19 8F 0C 44 99 22 20 9F 53 |)"5":.....D." .S|
000086F0: 4F 4C 55 54 49 4F 4E 3A 9A 20 9B 4D 55 4C 54 49 |OLUTION:. .MULTI|
00008700: 50 4C 59 20 42 4F 54 48 20 53 49 44 45 53 9A 20 |PLY BOTH SIDES. |
00008710: 42 59 20 35 2F 39 22 3A 99 00 37 8F 14 44 99 A6 |BY 5/9":..7..D..|
00008720: 31 31 29 22 9B 35 9A 20 20 20 20 9B 35 9A 28 39 |11)".5. .5.(9|
00008730: 29 20 20 9B 35 9A 22 00 55 8F 16 44 99 A6 31 31 |) .5.".U..D..11|
00008740: 29 22 9B C0 9A 46 20 3D 20 C0 C0 C0 C0 43 2B C0 |)"...F = ....C+.|
00008750: 28 33 32 29 22 00 75 8F 18 44 99 A6 31 31 29 22 |(32)".u..D..11)"|
00008760: 9B 39 9A 20 20 20 20 9B 39 9A 28 35 29 20 20 9B |.9. .9.(5) .|
00008770: 39 9A 22 3A 99 00 7F 8F 20 44 8D 38 35 31 30 00 |9.":.... D.8510.|
00008780: AE 8F 2A 44 99 22 20 9B 53 55 42 54 52 41 43 54 |..*D." .SUBTRACT|
00008790: 9A 20 35 28 33 32 29 2F 39 9B 20 46 52 4F 4D 20 |. 5(32)/9. FROM |
000087A0: 42 4F 54 48 20 53 49 44 45 53 9A 22 3A 99 00 CC |BOTH SIDES.":...|
000087B0: 8F 32 44 99 22 20 35 46 20 20 20 9B 35 28 33 32 |.2D." 5F .5(32|
000087C0: 29 9A 20 20 20 20 20 20 20 20 35 22 00 F2 8F 34 |). 5"...4|
000087D0: 44 99 22 20 C0 C0 20 9B 2D 20 C0 C0 C0 C0 C0 9A |D." .. .- ......|
000087E0: 20 3D 20 43 20 53 4F 20 C0 28 46 2D 33 32 29 3D | = C SO .(F-32)=|
000087F0: 43 22 00 12 90 36 44 99 22 20 39 20 20 20 20 9B |C"...6D." 9 .|
00008800: 39 9A 20 20 20 20 20 20 20 20 20 20 20 20 39 22 |9. 9"|
00008810: 3A 99 00 1C 90 3E 44 8D 38 35 31 30 00 4E 90 48 |:....>D.8510.N.H|
00008820: 44 99 22 20 9B 53 55 42 53 54 49 54 55 54 45 20 |D." .SUBSTITUTE |
00008830: 36 38 20 46 4F 52 20 46 9A 20 47 49 56 49 4E 47 |68 FOR F. GIVING|
00008840: 20 35 2F 39 28 36 38 2D 33 32 29 3D 43 22 00 7F | 5/9(68-32)=C"..|
00008850: 90 52 44 99 22 20 53 4F 20 43 3D 35 28 33 36 29 |.RD." SO C=5(36)|
00008860: 2F 39 20 3D 20 32 30 2E 20 4E 4F 57 20 59 4F 55 |/9 = 20. NOW YOU|
00008870: 20 54 52 59 2C 20 49 4E 20 54 48 45 22 3A 99 00 | TRY, IN THE":..|
00008880: B2 90 5C 44 99 22 20 46 4F 52 4D 55 4C 41 20 58 |..\D." FORMULA X|
00008890: 91 32 11 3D 59 2B 33 41 42 2C 20 46 49 4E 44 20 |.2.=Y+3AB, FIND |
000088A0: 41 20 57 48 45 4E 20 58 3D 35 2C 20 59 3D 34 22 |A WHEN X=5, Y=4"|
000088B0: 3A 99 00 D8 90 66 44 97 31 39 38 2C 30 3A 85 22 |:....fD.198,0:."|
000088C0: 20 26 20 42 3D 37 2E 20 41 3D 20 12 D2 22 3B 42 | & B=7. A= ..";B|
000088D0: 31 24 3A 99 22 92 93 22 00 F3 90 70 44 43 31 24 |1$:.".."...pDC1$|
000088E0: B2 22 31 22 3A 8B 42 31 24 B2 22 31 22 89 31 37 |."1":.B1$."1".17|
000088F0: 36 33 30 00 21 91 7A 44 99 22 20 4E 4F 20 4E 4F |630.!.zD." NO NO|
00008900: 54 20 22 42 31 24 22 2E 20 12 31 92 20 49 53 20 |T "B1$". .1. IS |
00008910: 43 4F 52 52 45 43 54 2E 20 57 45 27 4C 4C 22 3A |CORRECT. WE'LL":|
00008920: 99 00 49 91 84 44 99 22 20 4A 55 53 54 20 47 4F |..I..D." JUST GO|
00008930: 20 4F 56 45 52 20 54 48 49 53 3A 20 58 91 32 11 | OVER THIS: X.2.|
00008940: 3D 59 2B 33 41 42 22 3A 99 00 70 91 8E 44 99 22 |=Y+3AB":..p..D."|
00008950: 20 9B 53 55 42 54 52 41 43 54 20 59 20 46 52 4F | .SUBTRACT Y FRO|
00008960: 4D 20 42 4F 54 48 20 53 49 44 45 53 9A 22 3A 99 |M BOTH SIDES.":.|
00008970: 00 7A 91 98 44 8D 38 35 31 30 00 AE 91 A2 44 99 |.z..D.8510....D.|
00008980: 22 20 58 91 32 11 2D 59 3D 33 41 42 2E 20 4E 4F |" X.2.-Y=3AB. NO|
00008990: 57 20 9B 44 49 56 49 44 45 20 42 4F 54 48 20 53 |W .DIVIDE BOTH S|
000089A0: 49 44 45 53 9A 20 42 59 20 33 42 22 3A 99 00 B8 |IDES. BY 3B":...|
000089B0: 91 AC 44 8D 38 35 31 30 00 ED 91 B6 44 99 22 20 |..D.8510....D." |
000089C0: 28 58 91 32 11 2D 59 29 2F 33 42 20 3D 20 41 2E |(X.2.-Y)/3B = A.|
000089D0: 20 4E 4F 57 20 9B 53 55 42 53 54 49 54 55 54 45 | NOW .SUBSTITUTE|
000089E0: 9A 20 35 20 46 4F 52 20 58 2C 22 3A 99 00 1E 92 |. 5 FOR X,":....|
000089F0: C0 44 99 22 20 34 20 46 4F 52 20 59 20 26 20 33 |.D." 4 FOR Y & 3|
00008A00: 20 46 4F 52 20 42 20 47 49 56 49 4E 47 20 28 35 | FOR B GIVING (5|
00008A10: 91 32 11 2D 34 29 2F 33 28 37 29 22 3A 99 00 28 |.2.-4)/3(7)":..(|
00008A20: 92 C5 44 8D 38 35 31 30 00 54 92 CA 44 99 22 20 |..D.8510.T..D." |
00008A30: 57 48 49 43 48 20 45 51 55 41 4C 53 20 28 32 35 |WHICH EQUALS (25|
00008A40: 2D 34 29 2F 32 31 20 3D 20 32 31 2F 32 31 20 3D |-4)/21 = 21/21 =|
00008A50: 31 22 3A 99 00 60 92 CF 44 99 3A 8D 38 35 31 30 |1":..`..D.:.8510|
00008A60: 00 9C 92 D4 44 99 22 20 9F 52 45 56 49 45 57 3A |....D." .REVIEW:|
00008A70: 9A 20 54 48 45 20 56 41 52 49 41 42 4C 45 53 20 |. THE VARIABLES |
00008A80: 49 4E 20 45 3D 4D 43 91 32 11 20 41 52 45 20 4D |IN E=MC.2. ARE M|
00008A90: 2C 43 22 3A 99 3A 89 31 37 31 32 30 00 A6 92 DE |,C":.:.17120....|
00008AA0: 44 8D 39 30 30 30 00 D0 92 E8 44 99 22 20 4F 4B |D.9000....D." OK|
00008AB0: 20 22 41 31 24 22 20 4C 45 54 27 53 20 43 48 45 | "A1$" LET'S CHE|
00008AC0: 43 4B 20 54 48 49 53 20 4F 55 54 22 3A 99 3A 8E |CK THIS OUT":.:.|
00008AD0: 00 FE 92 40 9C 99 22 20 20 20 20 9F 54 48 45 20 |...@.." .THE |
00008AE0: 54 4F 50 49 43 53 20 46 4F 52 20 50 41 52 54 20 |TOPICS FOR PART |
00008AF0: 46 4F 55 52 20 41 52 45 3A 22 3A 99 3A 99 00 2D |FOUR ARE:":.:..-|
00008B00: 93 4A 9C 99 22 31 20 41 4C 47 45 42 52 41 20 49 |.J.."1 ALGEBRA I|
00008B10: 49 49 20 2D 20 46 55 52 54 48 45 52 20 46 41 43 |II - FURTHER FAC|
00008B20: 54 4F 52 49 53 41 54 49 4F 4E 22 3A 99 00 5A 93 |TORISATION":..Z.|
00008B30: 54 9C 99 22 32 20 41 4C 47 45 42 52 41 20 49 56 |T.."2 ALGEBRA IV|
00008B40: 20 20 2D 20 41 4C 47 45 42 52 41 49 43 20 46 52 | - ALGEBRAIC FR|
00008B50: 41 43 54 49 4F 4E 53 22 3A 99 00 7F 93 5E 9C 99 |ACTIONS":....^..|
00008B60: 22 33 20 41 4C 47 45 42 52 41 20 56 20 20 20 2D |"3 ALGEBRA V -|
00008B70: 20 45 51 55 41 54 49 4F 4E 53 22 3A 99 3A 99 00 | EQUATIONS":.:..|
00008B80: B0 93 68 9C 99 22 20 9B 48 41 56 45 20 59 4F 55 |..h.." .HAVE YOU|
00008B90: 20 41 4C 52 45 41 44 59 20 43 4F 4D 50 4C 45 54 | ALREADY COMPLET|
00008BA0: 45 44 20 41 4E 59 20 4F 46 20 54 48 45 22 3A 99 |ED ANY OF THE":.|
00008BB0: 00 D9 93 72 9C 99 22 20 41 42 4F 56 45 20 22 41 |...r.." ABOVE "A|
00008BC0: 31 24 22 2E 9A 20 41 4E 53 57 45 52 20 59 45 53 |1$".. ANSWER YES|
00008BD0: 20 4F 52 20 4E 4F 22 3A 99 00 F7 93 7C 9C 97 31 | OR NO":....|..1|
00008BE0: 39 38 2C 30 3A 85 01 01 01 01 01 01 01 01 01 01 |98,0:...........|
00008BF0: 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 |................|
00008C00: 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 |................|
00008C10: 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 |................|
00008C20: 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 |................|
00008C30: 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 |................|
00008C40: 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 |................|
00008C50: 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 |................|
00008C60: 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 |................|
00008C70: 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 |................|
00008C80: 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 94 |................|
00008C90: AE 9C 97 31 39 38 2C 30 3A 85 20 22 20 41 20 52 |...198,0:. " A R|
00008CA0: 45 56 49 45 57 3F 20 28 59 45 53 20 4F 52 20 4E |EVIEW? (YES OR N|
00008CB0: 4F 29 20 12 D2 D2 D2 22 3B 42 31 24 3A 99 22 92 |O) ....";B1$:.".|
00008CC0: 22 00 DA 94 B8 9C 8B 42 31 24 B2 22 59 45 53 22 |"......B1$."YES"|
00008CD0: A7 99 22 93 22 3A 89 31 35 30 00 EE 94 C2 9C 8B |..".":.150......|
00008CE0: 42 31 24 B2 |B1$. |
.......818,165:.775,168:.G(8).@....788,5
2:.787,64:.792,19:.793,3.J....3000.|....
".".14)"...COMPUTER TUTOR....":A1$."LEAR
NER".......7)".BASIC ARITHMETIC AND ALGE
BRA":....(...16)"PART FOUR":.:....-...11
)".COPYRIGHT (C) 1983."...2...20)".BY.."
...<...7)"JOHN C PAYNTER B.SC.,MAPSS.".$
.F...20)"&.".R.P...5)"MARY ANN PAYNTER B
.A.(HONS) SYD...."...Z.." PLEASE TYPE IN
YOUR FIRST NAME FOR ME.."...D..198,0:.
" .RRRRRRR";A1$:.".."...I.A1$.H(A1$,8)..
.N.." .VERY NICE TO SEE YOU AGAIN "A1$".
.."...X.." I AM ASSUMING THAT YOU HAVE C
OMPLETED.".'...." PART THREE!.".3.... 40
000.A...." THE FIRST TOPIC FOR PART FOUR
IS.":K.1......" .ALGEBRA III - FURTHER
FACTORISATION."... .." .................
....................".H....10000.T...X.0
:K.1.......7)".QUIZ ONE - FACTORISATION.
".......7)"..........................".O
.H.." .BE VERY CAREFUL TYPING IN YOUR AN
SWERS."..M.." SINCE ONE ERROR STARTS TH
E QUIZ OVER &."...R.." TWO ERRORS REQUIR
ES REVIEW!.".N.W.." .YOU MAY USE PENCIL,
PAPER AND A."......" CALCULATOR "A1$"..
."......A2.10. ..,...Q.1:." .USING THE F
ORMAT SHOWN, FACTORISE THE.".C...." FOLL
OWING:....".J....".1. 3X.2.+10X+3 .(RXR
R)(XRR).."......198,0:Z.0:. "
.";B1$:."..".....C1$."(3X+1)(X+3)":.B1$.
C1$..8090.F....Z.0.280.P....8020......:.
".2. 2X.2.-4X+2 .(RXRR)(XRR).". ."..198
,0:Z.0:. " .";B1$:."..".E.,.C1$
."(2X-2)(X-1)":.B1$.C1$..8090.R.6..Z.0.3
30.\.@..8020...J..:.".3. 5X.2.-3X-2 .(R
XRR)(XRR).."...T..198,0:Z.0:. "
.";B1$:."..".R.^.C1$."(5X+2)(X-1)":.B1$
.C1$..8090...H..Z.0.380...R..8020...|..:
.".4. 2X.2.+8X+6 .(RXRR)(XRR)..".:....1
98,0:Z.0:. " .";B1$:.".."._...C
1$."(2X+2)(X+3)":.B1$.C1$..8090.L....Z.0
.410.V....8020.....Q.2:.:.".5. 3XZ+6XY-2
Y-Z .(RXRR)(RYRR)..".R....198,0:Z.0:. "
.";B1$:."..".....C1$."(3X-
1)(2Y+Z)":.B1$.C1$..8090......Z.0.460...
B..8020.B.L..:.".6 FROM HSC 2 UNIT EXAM(
1980) 'FACTORISE.".Y.Q.." COMPLETELY'...
"...S.." 3X.2.-12Y.2. .R(XRRR)(XRRR).."
...V..198,0:Z.0:. " .";B1$:.".."
.....C1$."3(X+2Y)(X-2Y)":.B1$.C1$.B1$."3
(X-2Y)(X+2Y)"..8090......Z.0.500......80
20.+...Q.3:.:.".7. X.3.+Y.3. .(XRR)(X^R
RXYRR^R)..".Q....198,0:Z.0:. " .";
B1$:."..".|...C1$."(X+Y)(X^2-XY+Y^2)":.B
1$.C1$..8090......Z.0.540......8020.H...
.:.".8. 27X.3.-8Y.3. .(RXRRR)(RX^RRRXYR
RR^R).."...&..198,0:Z.0:. " .";
B1$:."..".!.0.C1$."(3X-2Y)(9X^2+6XY+4Y^2
)":.B1$.C1$..8090...:..Z.0.580.8.?..8020
._.D.Q.0:."......":..11)".END QUIZ ONE".
J.I..63200...N.." THE NEXT TOPIC IS:.":K
.2...Q.." .ALGEBRA IV - ALGEBRAIC FRAC
TIONS."...S.." .......................
..........."...U.Z.0:.14000...V.X.0:K.2.
*.X...4)".QUIZ TWO - ALGEBRAIC FRACTIONS
.".U.B...4)"............................
....".D.L.A2.10:.200.M.V.A2.0...~...12)"
3 . X+3"......".1 SIMPLIFY:. ... F ...
. .R.":..D.....12)"X-3 ... X.2.-9".S..
..198,0:Z.0...... "
....";B1$:."....."."...C1$."3":.B1$
.C1$..8090./....Z.0.698.9....8020.P.....
12)" 2X 3Y+3".|....".2 SIMPLIFY:. ...
. - ........... .R.".......12)"2X-3 2X
-3Y+2XY-3"...F..198,0:Z.0...P.. "
...";B1$:."....
"...Z.C1$."1":.B1$."1"..8090......Z.0.76
0......8020.2.....11)"......END QUIZ TWO
.".=....63200.^...." THE NEXT TOPIC IS:"
:K.3:......." .ALGEBRA V - EQUATI
ONS."......" ....................
..."... ..16000.C.%.X.0:K.3...*...7)".QU
IZ THREE - EQUATIONS.."...4.A2.10:.200..
.>.A2.0...H.." ALL QUESTIONS ARE FROM TH
E 1982 HSC 2.".Z.R.." UNIT MATHEMATICS E
XAMINATION (NSW)."...\..:.".1. SOLVE THE
EQUATION 2(X+3)=3(X-1)."...F..198,0:Z.0
:." X= .R";B1$:."..".G.P.C1$."9":.B1$.C1
$..8090.T.Z..Z.0.910......8020......".2.
IN THE FORMULA V.2.=U.2.-2FS, FIND S,."
.7...." GIVEN THAT V=3, U=4 AND F=-3..".
]....198,0:Z.0:." S= .RR/R";B1$:.".."...
..C1$."-7/6":.B1$.C1$.B1$."7/-6"..8090..
....Z.0.970......8020...J...10)"......EN
D QUIZ THREE.".I.T..63200...P.." .THIS C
OMPLETES PART FOUR....."...U.."IT'S BEEN
A REAL PLEASURE WORKING WITH.".C.Z.."YO
U. SEE YOU LATER "A1$"....".E.....25)".T
O EXIT.":.9300:.64738.K.......D.."..LOAD
ING TEST - CHECK BYTES:...".E.X.." ".(0)
.(.(0).0).65536" BYTES FREE...":.2020...
..."......NOTE: THE 'RUN/STOP' KEY WILL
NOT WORK.".).B.."WHILE THIS PROGRAM IS R
UNNING. TO EXIT.".W.L.."BEFORE THE END O
F THE PROGRAM, SIMPLY."...Q.."REMOVE THE
DISK FROM THE DISK DRIVE AND."...V.."TU
RN OFF YOUR COMPUTER. ALSO, YOU WILL."..
...."NOT BE ABLE TO CHANGE TO LOWER CASE
.."......"DON'T WORRY! ALL WILL BE BACK
TO NORMAL."......"WHEN WE FINISH.....".:
....9300:..M.T..".":.X.1.8040.J.Y.." I'M
SORRY, "B1$" IS."...^.." WRONG, ."C1$".
IS RIGHT..":X.1...C.." WE'LL START AGAI
N "A1$". REMEMBER."...D.." .ONE MORE ERR
OR WILL REQUIRE REVIEW..."...E..K.1.215.
..F..K.2.600...G..K.3.810.>.H.." I'M SOR
RY BUT THAT'S TWO ERRORS, WE.".Q.R.." HA
D BETTER GO BACK AND REVIEW FROM:.":.920
0.{....9000.....Z.1:.:.:.:....>!.L.1.400
0:.:L.0:....(#Y..(.(0).5):R.0.C.*#.Y.0.9
010.Q.+#.Y.1.9020...,#.Y.2.9030...-#.Y.3
.9040....#.Y.3.9050...2#." .SPOT ON "A1$
"!..":.63010.&.7#Y.0:..L.<#." .THAT'S RI
GHT "A1$"...":.63010.V.A#Y.0:....F#." .C
ORRECT "A1$"! GOOD ON YOU...":.63010...K
#Y.0:....P#." .VERY GOOD "A1$"!..":.6301
0...U#Y.0:....Z#." .YES "A1$", THAT'S CO
RRECT..":.63010..._#Y.0:..%.D#." .TREMEN
DOUS! VERY WELL DONE "A1$"!..":.63010.3.
I#Y.0:R.0:..Q..#." NO ."B1$". IS WRONG:.
"....#." .CHECK YOUR WORK. CHECK THE FOR
MAT OF."... #." YOUR ANSWER.. OK "A1$":.
"....#.....#.K.1.9205.B..#.K.2.593.O..#.
K.3.790....#.Q.1.150....#.Q.2..11190....
$.Q.3..12740.)..$." OK "A1$" LET'S TRY A
GAIN.":.:Q.0:.175.K.T$.198,0:..25)".PRES
S ANY KEY."._.^$.A$:.A$."".9310.P.H$."."
:A$."":.....'." .A. TRINOMIALS CONTINUED
:..".B..'." IN THE LAST SECTION WE COVER
ED HINTS."....'." ON FACTORISING QUADRAT
IC TRINOMIALS IF.".#.$'." A=1 IN AX.2.+B
X+C. WE WILL NOW CONSIDER.".R..'." FACTO
RISING .AX.2.+BX+C WHEN A IS ANY."...8'.
" PRIME NUMBER.. .PLEASE WRITE DOWN THES
E."...B'." STEPS AS WE GO "A1$"..."...L'
.9300...V'." .LET P & Q BE THE SECOND TE
RMS OF THE."...`'." FACTORS OF AX.2.+BX+
C.:.".,.J'.".1. IF A IS A PRIME NUMBER T
HE FACTORS.".].T'." ARE: (.AX.+P)(X+Q) W
HERE B=AQ+P & C=PQ.."...~'." APPLYING TH
E DISTRIBUTIVE LAW:."....'." (.AX.+P)(X+
Q)=AX.2.+AQX+PX+PQ =.".L..'..12)"=AX.2.+
(AQ+P)X+PQ.".. .'." SO TO FACTORISE .2X.
.2.+5X+2 THE TERMS ARE."., .'.198,0:. "
(.RR.+P)(X+Q) .RR";B1$:."..".@ .'.B1$."2
X".10190.} .'.B1$."AX". ." YES BUT IN TH
IS CASE AX=.2X. "A1$:.:.10140.. .'." NO
NOT "B1$". .2X. IS CORRECT. THE FAC-."..
D'." TORS OF 2X.2.+5X+2 ARE (.2X.+P) &
(X+Q).":.10070.. N'.9000."!X'.".2. AS BE
FORE IF B .&. C ARE POSITIVE THE.".Q!.'.
" SIGNS IN THE FACTORS ARE BOTH .+..":.:
...!.'." (AX.+.P)(X.+.Q)=AX.2..+.(AQ+P)X
.+.PQ [A IS PRIME":...!.'." B=.+.(AQ+P);
C=.+.PQ] SO TO FACTORISE":.:...!.(." 2X.
2..+.5X.+.2 THE SIGNS IN THE FACTORS ARE
":...".(.198,0:. " BOTH .R";B1$:."..".("
.(.B1$."+".10290.Y".(." NO "B1$" IS NOT
RIGHT. .+. IS CORRECT.":..."((." "A1$",
IF B .&. C ARE POSITIVE THE":.:.10210.."
2(.9000.N"<(.".3. IF .B IS NEGATIVE. .&
.C IS POSITIVE. THE":..."F(." SIGNS IN T
HE FACTORS ARE .BOTH. .-..":..0#P(." (AX
.-.P)(X.-.Q)=AX.2..-.AQX.-.PX.+.PQ ":.:.
.^#Z(..12)"=AX.2..-.(AQ+P)X.+.PQ [A IS P
RIME;"..#D(." B=.-.(AQ+P)X;C=.+.PQ] SO T
O FACTORISE:":.:..G#N(." 2X.2..-.5X.+.2
THE SIGNS IN THE FACTORS ARE":...#X(.198
,0:. " .BOTH. .R";B1$:.".."..#.(.B1$."-"
.10400./$.(." NO "B1$" IS NOT RIGHT, .-.
IS CORRECT.":..`$.(." IN THIS CASE B IS
NEGATIVE (-5) & C IS":...$.(." POSITIVE
(+2) SO "A1$", THE":.:.10310..$ (.9000.
J$.(.".4. IF .C. IS .NEGATIVE. THE SIGNS
IN THE":...%.(." FACTORS ARE .DIFFERENT
.. (AX.+.P)(X.-.Q) =":.:..<%.(." AX.2.-A
QX+PX.-.PQ = AX.2.+(P-AQ)X.-.PQ. SIMIL-"
:.:..W%H(." ARLY, (AX.-.P)(X.+.Q)=AX.2.+
(AQ-P)X.-.PQ SO TO":.:...%R(." FACTORISE
2X.2.-3X.-.2 THE SIGNS IN THE":..Y%.(.1
98,0:. " FACTORS ARE .RRRRRRRR";B1$:."..
"..%.(.B1$."DIFFERENT".10500..&.(." NOT
"B1$". .DIFFERENT. IS RIGHT.":..K&.(." C
HECK YOUR SPELLING "A1$".":.:.10410.U&.)
.9000..&.).".5. IF A IS A PRIME NUMBER,
THE SECOND":...&.)." TERMS OF THE FACTOR
S HAVE A .PRODUCT =C.":.:...&")." AND .A
Q+P=B.. SO CONSIDERING 2X.2.+.3.X+.2.":.
.!',)." THE SECOND TERMS OF THE FACTORS
HAVE A":..J'6).198,0:. " PRODUCT PQ = .R
";B1$:.".".]'@).B1$."2".10590..'J).".":.
" NO "B1$" IS NOT RIGHT. .2. IS CORRECT.
":.:..J'O)." AX.2.+BX+C HAS FACTORS (AX+
Q)(X+P) WHERE":.:...'T)." PQ=C, SO IN 2X
.2.+3X+2, PQ=.2. LET'S LOOK":..6(Y)." OV
ER THIS SECTION AGAIN. .WRITE DOWN THE":
.10050.@(^).9000.J(H).198,0:. " AND AQ
+P = .R";B1$:."..".}(R).B1$."3".10650..(
|)." NO, "B1$" IS NOT RIGHT, .3. IS CORR
ECT.":.:...(.)." AX.2.+BX+C HAS FACTORS
(AX+Q)(X+P) WHERE":.:...).)." AQ+P=B, SO
IN 2X.2.+3X+2, AQ+P=.3.. WE'LL":..R).).
" REVIEW THIS PART. .PLEASE WRITE DOWN T
HE":.10050.\).).9000.G).).50000..).)." .
EXAMPLE 1:. FACTORISE 2X.2.+5X+2":...).)
." .SOLUTION:.":...).).".1. (2X )(X )
SINCE A IS A PRIME NUMBER.":.8510..*B)."
.2. (2X.+. )(X.+. ) SINCE B=.+.5 & C=.+.
2":...*G).8510.S*L).".3. (2X.+1.)(X.+2.)
SINCE C=PQ=(2)(1)=2 AND":...*V)."
B=AQ+P=(2)(2)+1=5":.:...*.
).8510..*.)." NOW YOU TRY, FACTORISE 3X.
2.+7X+2":...*.).198,0:. " .(RRRR)(RRR)";
B1$:.".."..+.)C1$."(3X+1)(X+2)":.B1$.C1$
.B1$."(X+2)(3X+1)".10780.@+.)C2$."3X.2.+
6X+X+2":C3$."3X.2.+7X+2".O+.).R.1.10750.
Y+.).9100.H+.)R.1:.10720..+.)." NO, "B1$
" IS STILL WRONG.":...+.*." ."C1$". IS R
IGHT. "C1$"=":.:..P+.*." "C2$" = "C3$".
LET'S":...,.*." GO OVER THIS. .PLEASE WR
ITE DOWN THE":.:.10050..,.*.9060.<,&*."
.EXAMPLE 2:. FACTORISE 3X.2.-7X+2":..R,0
*." .SOLUTION:.":...,:*.".1. (3X )(X )
SINCE A IS A PRIME NUMBER":...,?*.8510.
D,D*.".2. (3X.-. )(X.-. ) SINCE B=.-.7 .
&. C=.+.2":..N,I*.8510..-N*.".3. (3X.-1.
)(X.-2.) SINCE C=PQ=(-1)(-2)=2 AND":..8-
X*." B=AQ+P=(3)(-2)+(-1)
=-7":.:..B-]*.8510.N-B*." NOW YOU TRY, F
ACTORISE 3X.2.-7X+4":...-L*.198,0:. " .(
RRRR)(RRR)";B1$:."..".P-V*C1$."(3X-4)(X-
1)":C2$."3X.2.-3X-4X+4":C3$."3X.2.-7X+4"
..-.*.B1$.C1$.B1$."(X-1)(3X-4)".10900...
.*.R.1.10890....*.9100....*R.1:.10850.(.
.*.10750.2..*.9000.^..*." .EXAMPLE 3:. F
ACTORISE 3X.2.+5X-2":..T..*." .SOLUTION:
.":.....*.".1. (3X )(X ) SINCE A IS A
PRIME NUMBER":.....*.8510....*.".2. (3X.
+..... )(X.+..... ) SINCE C=.-.2":....A*
.8510.$/F*.".3. (3X.-1.)(X.+2.) SINCE C=
PQ=(-1)(2)=-2 AND":..W/P*."
B=AQ+P=(3)(2)+(-1)=5":.:..A/U*.851
0../Z*." NOW YOU TRY, FACTORISE: 3X.2.+X
-4":.../.*.198,0:. " .(RRRR)(RRR)";B1$:.
".."../.*C1$."(3X+4)(X-1)":C2$."3X.2.-3X
+4X-4":C3$."3X.2.+X-4"..0.*.B1$.C1$.B1$.
"(X-1)(3X+4)".11020."0.*.R.1.10750.,0.+.
9100.;0.+R.1:.10970.E0.+.9060.V0.+." IN
OUR EXAMPLES SO FAR, ONE FACTOR HAS":...
0 +." BEEN (X+.....1.) OR (AX+.....1.).
LET'S LOOK AT":...0*+." ONE WHERE THIS I
S NOT THE CASE. .ALL":...14+." THE SAME
PRINCIPLES APPLY..":..21>+." .EXAMPLE 4:
. FACTORISE 3X.2.+10X+8":..H1H+." .SOLUT
ION:.":..R1R+.".1. (3X )(X ) SINCE A I
S PRIME":...1W+.L.1.8000:...1\+.".2. (3X
.+. )(X.+. ) SINCE B=.+.10 & C=.+.8":...
1A+.8510..1F+.".3. (3X.+4.)(X.+2.) SINCE
C=PQ=(4)(2)=8 AND":..'2P+."
B=AQ+P=(3)(2)+4=10":.:..12U+.851
0.^2Z+." NOW YOU TRY, FACTORISE 5X.2.+17
X+6":...2.+.198,0:. " .(RRRR)(RRR)";B1$:
."..".G2.+C1$."(5X+2)(X+3)":C2$."5X.2.+1
5X+2X+(2)(3)":C3$."5X.2.+17X+6"..2.+.B1$
.C1$.B1$."(X+3)(5X+2)".11180..2.+.R.1.10
750..3.+.9100..3.+R.1:.11130..3.+.9000.@
3.+." .B. GROUPING OF TERMS:.":..R3.+."
AGAIN WE ARE DEALING WITH THE .DISTRIB-"
:...3J+." UTIVE LAW. IN REVERSE. RECALL
THAT":..Y3T+." .A.(B+C).=.A.B+.A.C.. NOW
SUPPOSE THAT .A=X+Y..":...4.+." THEN .(
X+Y).(B+C).=.(X+Y).B+.(X+Y).C. & EXPAND-
".M4.+." ING THESE TERMS GIVES .B.X.+.B.
Y.+.C.X.+.C.Y. SO TO"..4.+." .FACTORISE.
BX+BY+CX+CY WE PERFORM THESE":...4.+."
TWO STEPS IN REVERSE. THAT IS BX+BY+CX":
...4.,.198,0:." +CY=B.(X+Y).+C.(RRR)";B1
$:.".."..4.,C1$."(X+Y)":.B1$.C1$.11320.(
5.,." I'M SORRY "B1$" IS NOT CORRECT.":.
.S5$,." ."C1$". IS CORRECT. REMEMBER "A1
$:...5.,." WE ARE SIMPLY DEALING WITH TH
E .DISTRIB-":.11210..58,.9000.G5B,." AND
B(X+Y)+C(X+Y) HAS A .COMMON FACTOR.":..
.5L,." (X+Y), SO TO FACTORISE WE WRITE:"
:..#6V,." (X+Y)(B+C). SO B.(X+Y).+C.(X+Y
). HAS A":..T6`,.198,0:. " COMMON FACTOR
OF .(RRR)";B1$:.".".S6J,C1$."(X+Y)":.B1
$.C1$.11390..6T,.".":.11290..6~,.9000..6
.,." OF COURSE "A1$" THE TERMS ARE NOT":
...6.,." OFTEN GIVEN TO US IN ORDER,SO W
E .GROUP.":...7.,." TERMS IN PAIRS WHICH
HAVE A COMMON":..P7.,." FACTOR. .C.X+.B
.Y+.B.X+.C.Y MIGHT BE GROUPED":...7.,."
.B.X+.B.Y+.C.X+.C.Y = .B.(X+Y)+.C.(X+Y)"
:...7D,.198,0:. " AND THIS EQUALS (X+Y).
(RRR)";B1$:.".."..7N,C1$."(B+C)":.B1$.C1
$.B1$."(C+B)".11490..7X,.11290..7.,.9000
./8.,." NOW B.X.+B.Y.+C.X.+C.Y. COULD AL
SO HAVE BEEN":..J8.,." GROUPED B.X.+C.X.
+B.Y.+C.Y. WHICH .STILL. YIELDS":...8.-.
" (X+Y)(B+C). THE IMPORTANT THING TO RE-
":..F8.-." MEMBER "A1$",IS TO REARRANGE
THE":...8.-." TERMS TO GIVE .PAIRS. WITH
.COMMON FACTORS.".(9.-." NOW YOU TELL M
E. TO FACTORISE TERMS":..W9(-." LIKE CX+
BY+BX+CY YOU REARRANGE TERMS":...92-." S
O THAT YOU ARE LEFT WITH .PAIRS. WHICH":
...9<-.198,0:. " HAVE .RRRRRR RRRRRRR";B
1$:.".."..9F-C1$."COMMON FACTORS":.B1$.C
1$.11610..:K-.B1$."A COMMON FACTOR".1161
0..:P-.11290..:Z-.9000.G:D-." WHEN YOU '
TAKE OUT' COMMON FACTORS YOU":..Z:N-." A
RE JUST APPLYING THE .DISTRIBUTIVE. LAW"
:...:X-." IN REVERSE. SO BX+CX+BY+CY =":
..R:.-." X(B+C)+Y(B+C) = (X+Y)(B+C) IS J
UST AP-":...;.-." PLYING THE .RRRRRRRRRR
RR. LAW IN REVERSE":..-;.-.198,0:. " .RR
RRRRRRRRRR";B1$:."..".J; -C1$."DISTRIBUT
IVE":.B1$.C1$.B1$."DISTRIBUTIVE LAW".117
00.U;.-.11290.;.-.9000..;.-." LET'S LOO
K AT SOME EXAMPLES "A1$:..V;H-." .EXAMPL
E 1:. FACTORISE 3X+ZY+ZX+3Y":...;R-." .S
OLUTION:.":...<.-.".1. 3X+3Y+ZX+ZY (GR
OUP INTO PAIRS WITH":..G<.-."
COMMON FACTORS).".Q<.-.8510..<.-."
.2. 3(X+Y)+Z(X+Y) (3 & Z ARE THE COMMON"
:...<.-." FACTORS)."..<.
-.8510..<...".3. (X+Y)(3+Z) [(X+Y) IS
A COMMON FAC-":...<...," TOR]":..
.=...8510.0=..." NOW YOU TRY, FACTORISE
2XY+RY+RP+2XP":..W="..198,0:. " .(RRRR)(
RRR)";B1$:.".."..=,.C1$."(2X+R)(Y+P)":C2
$.".2X.Y+.2X.P+.R.Y+.R.P":C3$.".2X.(Y+P)
+.R.(Y+P)".G=6..B1$.C1$.B1$."(Y+P)(2X+R)
".11870..=8..B1$."(2X+R)(P+Y)".B1$."(P+Y
)(2X+R)".11870.%>:..B1$."(R+2X)(Y+P)".B1
$."(Y+P)(R+2X)".11870.T><..B1$."(R+2X)(P
+Y)".B1$."(P+Y)(R+2X)".11870.C>=..R.1.11
840.M>>..9100.|>?.R.1:.11800..>@.." NO "
B1$" IS STILL WRONG.":..C>J.." ."C1$". I
S CORRECT. GROUP":...>O.." INTO PAIRS: "
C2$" GIVING":...?T.." "C3$" = "C1$".":.:
.11620..?^..9000.??H.." .SINCE A=(1)(A),
1 IS OFTEN A COMMON":..L?R.." FACTOR SO
WATCH OUT FOR IT "A1$"..":...?|.." .EXA
MPLE 2:. FACTORISE 3XY+Y+3XZ+Z":...?..."
.SOLUTION:.":...?...".1. 3XY+3XZ+(1)Y+(
1)Z (GROUP INTO PAIRS":...@....18)"WITH
COMMON FACTORS)":...@...L.1.6000:..A@...
".2. 3X(Y+Z)+1(Y+Z) (3X & 1 ARE COMMON":
..W@....18)"FACTORS)":..A@...8510..@..."
.3. (3X+1)(Y+Z) [(Y+Z) IS A COMMON":.
..@B...18)"FACTOR]":...@G..8510..@L.." N
OW YOU TRY, FACTORISE P+5XQ+5XP+Q":...AV
..198,0:. " .(RRRR)(RRR)";B1$:."..".NA..
C1$."(5X+1)(P+Q)":C2$.".5X.P+.5X.Q+.1.P+
.1.Q":C3$.".5X.(P+Q)+.1.(P+Q)".SA...B1$.
C1$.B1$."(P+Q)(5X+1)".12030..A...B1$."(5
X+1)(Q+P)".B1$."(Q+P)(5X+1)".12030.QA...
B1$."(1+5X)(P+Q)".B1$."(P+Q)(1+5X)".1203
0..B...B1$."(1+5X)(Q+P)".B1$."(Q+P)(1+5X
)".12030..B...R.1.11840..B...9100.(B..R.
1:.11980.2B...9000.AB./." .IF THERE ARE
NEGATIVE SIGNS BE VERY":...B./." CAREFUL
WHEN YOU REARRANGE TERMS!.":...B./." .E
XAMPLE 3:. FACTORISE 6XY-Y+Z-6XZ":..QB&/
." .SOLUTION:.":...B0/.".1. 6XY-6XZ-Y+Z
(GROUP INTO PAIRS":..!C:/..18)"WITH C
OMMON FACTORS)":..1CD/.L.1.6000:..FCN/."
.2. 6X(Y-Z).-1.(Y.-.Z) (6X & -1 ARE FACT
ORS":...CX/..18)".NOTE.:-1(Y-Z)=-Y+Z)":.
..CB/.8510..CL/.".3. (6X-1)(Y-Z) (Y-Z
IS A COMMON":..UCV/..17)" FACTOR)":...C
{/.8510..D./." NOW YOU TRY, FACTORISE IN
SIMPLEST":..'D./." FORM 2XP-P+Q-2XQ":..
ND./.198,0:. " .(RRRR)(RRR)";B1$:.".."..
D./C1$."(2X-1)(P-Q)":C2$."2XP-2XQ-P+Q":C
3$."2X(P-Q).-1.(P.-.Q)"..D./.B1$.C1$.B1$
."(P-Q)(2X-1)".12210.CD./.R.1.11840.MD./
.9100..D./R.1:.12160..D./.9000..E./." .B
E VERY CAREFUL WHEN GROUPING IN PAIRS":.
.HEF/." AND REMEMBER NOT ALL EXPRESSIONS
WILL":..WEP/." FACTORISE!. FOR EXAMPLE,
AX+AY+BX+BZ":...EZ/." A FIRST STEP MIGH
T BE A(X+Y)+B(X+Z).":..WE./." FURTHER ST
EPS ARE .NOT. POSSIBLE SINCE":...F./." T
HERE ARE .NO COMMON FACTORS.. A DOES":..
3F./." EQUAL B & (X+Y) IS NOT (X+Z). CAN
":..DF.0." XY+XZ+BY+BX BE FACTORISED? (A
NSWER YES":...F.0.198,0:. " OR NO) .RR";
B1$:.".."..F.0.B1$."NO".12330.VF 0." SOR
RY BUT .NO. IS CORRECT..REMEMBER TO.":.:
.12220..F*0.9000..G40." . THE COMMON FAC
TORS ARE NOT ALWAYS":..>G>0." OBVIOUS. F
OR INSTANCE 12XY & 3XZ HAVE":..`GH0." A
COMMON FACTOR OF 3X..":...GR0." .EXAMPLE
4:. FACTORISE 6XY+2XZ-3Y-Z":...G\0." .S
OLUTION:.":..WGF0.".1. 6XY+2XZ-3Y-Z
(GROUP IN PAIRS WITH":...GP0..20)"COMMON
FACTORS)":...HU0.L.1.6000:..6HZ0.".2. 2
X(3Y+Z)-1(3Y+Z) (2X & -1 ARE COMMON":..L
H.0..20)"FACTORS)":..VH.0.8510..H.0.".3.
(2X-1)(3Y+Z) [(3Y+Z) IS A COMMON":.
..H.0..20)"FACTOR]":...H.0.8510.TH.0." N
OW YOU TRY, FACTORISE IN SIMPLEST":...H.
0." FORM 12XY-Z+3YZ-4X":...I.0.198,0:. "
.(RRRR)(RRRR)";B1$:."..".[I.0C1$."(4X+Z
)(3Y-1)":C2$."12XY-4X+3YZ-Z":C3$."4X(3Y-
1)+Z(3Y-1)"..I.0.B1$.C1$.B1$."(3Y-1)(4X+
Z)".12510..IJ0.B1$."(Z+4X)(3Y-1)".B1$."(
3Y-1)(Z+4X)".12510.AIO0.R.1.11840.KIT0.9
100.ZIY0R.1:.12450..I.0.9060..J.0." .IT
IS ALSO IMPORTANT TO WATCH OUT FOR":..CJ
.0." COMMON EXPRESSIONS LIKE A.2.-B.2...
":..RJ.0." .EXAMPLE 5:. FACTORISE A.2.-B
.2.-A-B":...J.1." .SOLUTION:.":...J.1.".
1. (A+B)(A-B)-1(A+B) [SINCE A.2.-B.2.=":
..RJ.1..21)"(A+B)(A-B)]":...J$1.L.1.7000
:...K.1.".2. (A+B)(A-B-1+.............R.
....PZZP...2..W..3.........P....2..V..;.
.....V..3...P...P...........P.R...R...RZ
.......2.ZV..3...P....'.G....'.F+Y":...K
`1.198,0:. " .(RRR)(RRRRR)";B1$:.".."..K
J1C1$."(X+Y)(X-Y+1)":C2$."X.2.-Y.2.+X+Y"
:C3$.".(X-Y).(X+Y).+1.(X+Y)"..LT1.B1$.C1
$.B1$."(X-Y+1)(X+Y)".12730.CL~1.B1$."(X+
Y)(X+1-Y)".B1$."(X+1-Y)(X+Y)".12730.TL.1
.B1$."(X+Y)(1+X-Y)".B1$."(1+X-Y)(X+Y)".1
2730..L.1.B1$."(Y+X)(X-Y+1)".B1$."(X-Y+1
)(Y+X)".12730.VL.1.B1$."(Y+X)(X+1-Y)".B1
$."(X+1-Y)(Y+X)".12730..M.1.B1$."(Y+X)(1
+X-Y)".B1$."(1+X-Y)(Y+X)".12730.8M.1.B1$
."(X+Y)(1-Y+X)".B1$."(1-Y+X)(X+Y)".12730
.IM.1.B1$."(Y+X)(1-Y+X)".B1$."(1-Y+X)(Y+
X)".12730.XM.1.R.1.11840..M.1.9100..M.1R
.1:.12620..M.1.9000.DMD1." .C. SUM & DIF
FERENCE OF CUBES.":...MN1." AGAIN WE ARE
SIMPLY APPLYING THE DIST-":..&NX1." RIB
UTIVE LAW. .WRITE DOWN THESE FORMU-":..E
N.1." LAE AS WE GO "A1$"!.":..{N.1.".1.
A.3.+B.3.=(A+B)(A.2..-.AB+B.2.) SINCE:":
.:...N.1." .(A+B).(A.2.-AB+B.2.)=.A.(A.2
.-AB+B.2.)+.B.(A.2.-AB+B.2.)":...O.2." =
A.3..-.A.2.B.+.AB.2..+.BA.2..-.AB.2..+.B
.3. (COLLECT LIKE":.:..O.2..OO.2." =A.3
..-.A.2.B.+.BA.2..+.AB.2..-.AB.2..+.B.3.
.TERMS)":.:..ZO.2.198,0..O.2.". =A.3.
+B.3. (NOTE: BA.2.=A.2.B).":.9300..O(2."
.THE FORMAT FOR YOUR ANSWERS TO THE":..
.O22." NEXT FEW QUESTIONS IS IMPORTANT A
ND":...P72." MUST FOLLOW THIS EXAMPLE:."
:.:..+P<2." FACTORISE A.3.+B.3.:":..`PF2
." .(ARR)(A^RRRRRRRR)?. .(A+B)(A^2-AB+B^
2).":.:...PP2." NOW YOU TRY, FACTORISE X
.3.+Y.3.":...PZ2.198,0:. " .(XRR)(X^RRRR
RRRR)";B1$:."..".TPD2C1$."(X+Y)(X^2-XY+Y
^2)"..PN2.B1$.C1$.12940..QX2." NOT "B1$"
I WANTED":..-Q.2." ."C1$". REMEMBER "A1
$",":.:.12750.7Q.2.9000.RQ.2." SIMILARLY
, A.3.-B.3.=(A-B)(A.2.+AB+B.2.) SINCE":.
:...Q 2." .(A-B).(A.2.+AB+B.2.)=.A.(A.2.
+AB+B.2.).-B.(A.2.+AB+B.2.)":...Q.2." =A
.3..+.A.2.B.+.AB.2..-.A.2.B.-.AB.2..-.B.
3.":.:..4R.2." =A.3..+.A.2.B.-.A.2.B.+.A
B.2..-.AB.2..-.B.3.=.A.3.-B.3..":.:.._R.
2." NOW YOU TRY, FACTORISE X.3.-Y.3.":..
.RH2. 198,0:. " .(XRR)(X^RRRRRRRR)";B1$:
.".."..RR2C1$."(X-Y)(X^2+XY+Y^2)":.B1$.C
1$.13030.CR.2.12920.MR.2.9000..R.2." .EX
AMPLE 1:. FACTORISE X.3.+8":.:..*S.2." .
SOLUTION:. IN THE FORMULA A.3.+B.3. =":.
:..ZS.3." (A+B)(A.2.-AB+B.2.), A=X & B=2
, SO:":.:...S.3." X.3.+8=X.3.+2.3.=(X+2)
(X.2.-X(2)+2.2.)":.:...S.3." =
(X+2)(X.2.-2X+4)":.:...S"3." NOW YOU TRY
, FACTORISE Y.3.+27 .(USE Y^2":.:...S,3.
" FOR Y.2.).":..*T63.198,0:. " .(YRR)(Y^
RRRRRR)";B1$:."..".ST@3C1$."(Y+3)(Y^2-3Y
+9)":.B1$.C1$.13140.TTA3.B1$."(Y+3)(Y^2-
Y3+9)".13140..TE3.R.1.12920..TJ3.9100..T
O3R.1:.13090..TT3.9060.VT^3." .EXAMPLE 2
:. FACTORISE 27X.3.-8Y.3.":.:...UH3." .S
OLUTION:. IN THE FORMULA A.3.-B.3. A=3X
&":.:..AUR3." B=3Y SO 27X.3.-8Y.3.=(3X).
3.-(2Y).3. =":.:..WU|3." (3X-2Y)[(3X).2.
+(3X)(2Y)+(2Y).2.] WHICH =":.:...U.3." (
3X-2Y)(9X.2.+6XY+4Y.2.). NOW YOU TRY,":.
:...U.3." FACTORISE 8X.3.-Y.3. .(RXRR)(R
X^RRRRRRRRR).":...V.3.198,0:. "
.";B1$:."..".*V.3C1$."(2X-Y)(4X^2
+2XY+Y^2)".XV.3.B1$.C1$.B1$."(2X-Y)(4X^2
+2YX+Y^2)".13240.GV.3.R.1.12920.QV.3.910
0..V.3R.1:.:.13200..V.3.9000..VB3." IT L
OOKS LIKE YOU CAN HANDLE FACTOR-":...VL3
." ISATION NOW, WE'LL JUST MAKE SURE":..
.WV3." WITH A SHORT QUIZ. .TAKE YOUR TIM
E WITH":..IW.3." EACH QUESTION AND TYPE
ALL ANSWERS IN":..{W.3." THE FORMAT SHOW
N IN THE QUESTION, I.E..":.. W.3." .(RXR
R)., .(R^R). ETC.":.:.:...W.3.9300..W.4.
..W.6." AN .ALGEBRAIC FRACTION. IS SIMPL
Y A FRAC-"..X.6." TION WHOSE .DENOMINATO
R. IS AN ALGEBRAIC":..EX.6." EXPRESSION.
NOW YOU TELL ME, A FRACTION".VXD6." IN
WHICH THE .DENOMINATOR. IS AN ALGE-":...
XN6." BRAIC EXPRESSION IS REFERRED TO AS
AN":..SXX6.198,0:. " .RRRRRRRR RRRRRRRR
";B1$:.".."..X.6C1$."ALGEBRAIC FRACTION"
:.B1$.C1$.14080."Y.6." NO "B1$" IS NOT C
ORRECT.":..LY.6." ."C1$". IS CORRECT SIN
CE":.:.14000.VY.7.9000..Y.7." SO 3/(X+2)
IS AN ALGEBRAIC FRACTION":...Y.7." SINC
E IT HAS THE ALGEBRAIC EXPRESSION":...Y.
7." X+2 IN THE .DENOMINATOR.. (X+2)/3 IS
NOT":...Z(7." SINCE THE DENOMINATOR (3)
IS .NOT. AN":..FZ27." ALGEBRAIC EXPRESS
ION. IS 3/(X.2.) AN":...Z<7.198,0:. " AL
GEBRAIC FRACTION (YES OR NO).RRR";B1$:."
."..ZF7.B1$."YES".14170.RZP7.".":." 3/(X
.2.) .IS. AN ALGEBRAIC FRACTION!":.:.140
00..ZZ7.9000..[D7." IS (X.2.+Y.2.)/2 AN
ALGEBRAIC FRACTION":..7[N7.198,0:. " (YE
S OR NO) .RR";B1$:."..".K[X7.B1$."NO".14
220.|[.7." NO IT IS .NOT., THE DENOMINAT
OR (2) IS":...[.7." .NOT. AN ALGEBRAIC E
XPRESSION.":.:.14000..[.7.9000..[.7." .T
HE SAME LAWS APPLY TO ALGEBRAIC FRAC-":.
..\ 7." TIONS AS THEY DO TO ARITHMETIC F
RAC-":..5\.7..13)".24 (12)(2) 12".E\
.7." .TIONS.. E.G. .. = ....... = ..V2=1
V2=2"..\.7..13)"12 (12) 12":...\.
7." .12 IS A COMMON FACTOR.. SIMILARLY:"
:..J\.7." 2X (2)(X) X"..\.7." .. = .
..... = . V 2 = 1V2=2. .X IS A."..].7."
X (X) X":..F]H7." .COMMON FACTOR
.. SO TO .SIMPLIFY. ALGEBRAIC".W]R7." FR
ACTIONS WE LOOK FOR .COMMON FACTORS.":..
.].7." IN THE NUMERATOR & THE DENOMINATO
R. TO":..W].7." SIMPLIFY X(.X+2.)/(.X+2.
) THE COMMON":...^.7.198,0:. " FACTOR IS
.RRR";B1$:."..".)^.7C1$."X+2":.B1$.C1$.
B1$."(X+2)".14340.T^.7." NO, NOT "B1$".
."C1$". IS RIGHT.":..K^.7.L.1.1500:.:.14
230.U^.8.9000..^.8." AND (X+2)/(X+2) = 1
, SO [X(X+2)]/(X+2)":..U^.8." = (X)(1)=X
. NOW YOU TRY, SIMPLIFY:":.:..._"8.198,0
:. " [X(X.2.-3X)]/(X.2.-3X) .R";B1$:."."
.#_,8C1$."X":.B1$.C1$.14400.3_68.".":.14
330.=_@8.9000.I_J8." OF COURSE THE EXPRE
SSIONS ARE NOT":..._T8." USUALLY SO OBVI
OUS & MUST NORMALLY BE":..K_^8." .FACTOR
ISED.. SO TO SIMPLIFY AN ALGEBRAIC".._H8
." FRACTION, IT USUALLY HAS TO FIRST BE"
:.. `R8.198,0:. " .RRRRRRRRRR";B1$:.".."
.D`|8C1$."FACTORISED":.B1$.C1$.14480.U`.
8." NOT "B1$" THE CORRECT ANSWER IS":.:.
14430.`.8.9000..`.8." .EXAMPLE:. SIMPLI
FY (3X.2.-7X-6)/(X-3)":.:...`.8." .SOLUT
ION:. (3X.2.-7X-6)/(X-3) =":...A.8.".1.
[(3X+2)(X-3)]/(X-3)= FACTORISING":.:..'
A.8.,," 3X.2.-7X-6".1A.8.8510.MA.8.,
," ---------------".LA.8.," X-3","
(X-3) IS A"..AB8.".2. (3X+2) V ...="..A
D8.," X-3"," COMMON FACTOR":...AL8.8
510..AV8.".3. 3X+2 SINCE (X-3)/(X-3) = 1
.":.:...A.8.8510..B.8." NOW YOU TRY, SIM
PLIFY (2X.2.-7X+6)/(X-2)":..;B.8.198,0:.
" .RRRR";B1$:."..".FB.8C1$."2X-3":.B1$.
C1$.B1$."(2X-3)".14630.UB.8.R.1.14620.B
.9.9100..B.9R.1:.14560..B.9.14330..B&9.9
000.SB09." .TO MULTIPLY & DIVIDE ALGEBRA
IC FRAC-":...C:9." TIONS WE FACTORISE WH
ERE POSSIBLE AND":..4CD9." FOLLOW THE US
UAL RULES OF ARITHMETIC..":..LCL9..19)"
2 X.2.-4".UCN9." .EXAMPLE:. SIMPLIFY
... V .... ="..CP9..19)"X+2 4X":...CS
9.8510..CV9..11)"2(X.2.-4) 2.(X+2).(X-
2)"..CX9." .SOLUTION:. ....... = .......
... ="..DZ9..11)"4X(X+2) 4X.(X+2).":
...D]9.8510..D`9..11)".2.(X-2) X-2".G
DB9..11)"....... = ...".CDD9..11)".2.(2)
(X) 2X":..MDG9.8510..DJ9..23)"2X+1 1
2X.2.Y-6XY"..DL9." NOW YOU TRY, SIMPLIFY
.... V .........":...DN9..23)" XY
12X.2.-3":...EV9.198,0:R.0:. " .(USE PEN
& PAPER). = .R";B1$:."..".(E.9.B1$."
2".14740.;E.9Z.1:R.1:.14760.EE.9.9060.ZE
.9.Z.1.." .YOU'VE GOT IT THIS TIME!.":Z.
0:.:.14870..E.9." SO THE STEPS TO TAKE A
RE:":...E.9.14780.XE.9." NO .2. IS THE C
ORRECT ANSWER. .WRITE":...F.9." DOWN THE
SE STEPS AS WE GO "A1$"..":..-F.9.".1. .
FACTORISE WHERE POSSIBLE..":..]FD9." 2X+
1 12X.2.Y-6XY 2X+1 (6)(XY)(2X-1)"..F
F9." ....V......... = .... V ...........
..":...FH9." XY 12X.2.-3 XY 3
(2X+1)(2X-1)":..IFK9.8510..FP9.".2. .MUL
TIPLY & LOOK FOR COMMON FACTORS":.. GX9.
.16)" .(2X+1).(6).(XY).(2X-1).".AGZ9..1
6)"= ...................".IG.9..16)" .(
XY).(3).(2X+1).(2X-1).":..SG.9.8510..G.9
.".3. .DIVIDE COMMON FACTORS (A/A =1).":
...G.9..16)"= 6/3 = .2..".EG.9.:.9300.TG
.:.R.0.14870..H.:." REMEMBER, TO .SIMPLI
FY. ALGEBRAIC":.:.14290.7H.:." .YOU SHOU
LD RECALL FROM PART TWO THAT":..MH :." T
O DIVIDE BY A FRACTION (.C./.D.) .WE MUL
T-":...H*:." IPLY BY ITS RECIPROCAL (.D.
/.C.). .EXAMPLE:.":..GH2:." 2 . X+4
2 X.2.-4"..H4:.".1. ... F .... = .
.. V ....":...I6:." X-2 ... X.2.-4 X-
2 X+4":...I>:.8510.EIH:.".2. .FACTORIS
E WHERE POSSIBLE..":..`IP:." 2 (X+
2)(X-2)".{IR:." = ... V .........."..IT:
." X-2 X+4":...I\:.8510.QIF:.".3.
.MULTIPLY & LOOK FOR COMMON FACTORS..":
...IN:." 2(X+2).(X-2). 2(X+2) 2X+4
".'JP:." = ........... = ...... = .... N
OW YOU".QJR:." .(X-2).(X+4) X+4
X+4":..GJX:..15)" 12 . 3X-9"..JZ:." T
RY, SIMPLIFY ... F.... .... .R.":..LJ|:.
198,0:. " X+3 X.2.-9 ..
.";B1$:.".."..J.:.B1$."4".15090..K.:." I
'M SORRY "A1$" BUT .4. IS CORRECT":..7K.
:." .WRITE DOWN THESE STEPS PLEASE..":..
ZK :." 12 . 3X-9 12 X.2.-9"..K.:.
".1. ... ..... .... = ... V ....":...K.:
." X+3 X.2.-9 X+3 3X-9":..PK.:.".
2. .FACTORISE WHERE POSSIBLE.":...K.:."
(4)(3) (X-3)(X+3)"..L.:." = ...... V
..........".)L.:." X+3 3(X-3)":
..[L.:.".3. .MULTIPLY & LOOK FOR COMMON
FACTORS.":..ZLH:." (4).(3).(X-3).(X+3)
."..LJ:." = ................ = .4.. WE H
AD BETTER".ILL:." .(X+3).(3).(X-3).":
...LT:." REVIEW THIS MATERIAL "A1$".":..
.L.:.9300..M.:.14640..M.:.9000.<M.:." .R
ECALL FROM PART ONE:. 2/3 - 1/4 =":..KM.
;." 2 4 1 3 (2)(4)-(1)(3) 8-3
5"..M.;." . V . - . V . = .............
= ...=..".KM.;." 3 4 4 3 (3)
(4) 12 12":...M.;..12)"3X+1 X
3X+1 4 X 3".#N.;." .SIMILARLY:. .
... - . = .... V . - . V .".LN.;..12)"
3 4 3 4 4 3":..QN.;." (3X
+1)(4)-(X)(3) 12X+4-3X"..N.;." =......
.......... = ........=.(9X+4)/12.".FN.;.
" (3)(4) 12":...N";..23)
"2X+1 3X"..O$;." NOW YOU TRY, SIMPLIFY
.... - .."..O&;..23)" 3 5":..PO.;.
198,0:. " .USE THIS FORMAT. .(RRR)/RR";B
1$:.".."..O8;C1$."(X+5)/15":.B1$.C1$.B1$
."(5+X)/15".15210..OB;.R.1.15200..OL;.91
00..OV;R.1:.15138..O`;.14330..OJ;.9000..
OT;." .TO ADD OR SUBTRACT ALGEBRAIC FRAC
TIONS":.. P~;." FACTORISE WHERE POSSIBLE
& FOLLOW THE":..PP.;." USUAL RULES OF A
RITHMETIC. .EXAMPLE:.":..GP.;..10)" X-1
X"..P.;." SIMPLIFY .... - .......":
...P.;..10)"X.2.-1 X.2.+2X+1":..QP.;."
.1. .FACTORISE WHERE POSSIBLE.":...P.;."
X-1 X"..Q.;." = ........
.. - ..........".4Q.;." (X+1)(X-1) (
X+1)(X+1)":..DQ.;.L.1.6000:..OQ.;.".2. .
FIND THE COMMON DENOMINATOR.":...QB;."
(X-1)(X+1)-X(X-1)"..QD;." = ...........
......".DQF;." (X+1)(X+1)(X-1)":...QN
;.". .COPY THESE STEPS THEN.":.9300..RX;
.".3. .SIMPLIFY WHERE POSSIBLE & LOOK FO
R":..6R.;." COMMON FACTORS.":..]R.;."
(X-1)(X+1-X) .(X-1).(1)"..R.;." = .
.............. = ..............."..R.;."
(X+1)(X+1)(X-1) (X+1)(X+1).(X-1).":
...R.;." = .1/[(X+1)(X+1)]. NOW TRY THIS
FROM THE":...S.;." HSC EXAMINATION (197
9). EXPRESS":..)S.;." X+1 X-1".YS.<."
.... - .... AS A FRACTION IN ITS LOWEST
".SS.<." X.2.-X X.2.+X":...S.<." TERMS
. .NOTE USE OF / [ ETC IN TYPING":...S.<
." YOUR ANSWER..":...S.<.198,0:. " .R/[(
XRR)(XRR)]";B1$:."..".$T.<C1$."4/[(X-1)(
X+1)]":.I(B1$,2).")]".J(B1$,2,3)."/[(".1
5420.?T#<." ."B1$" IS IN THE":..QT(<." .
INCORRECT FORMAT PLEASE TYPE ANSWER AS":
...T-<." SHOWN BELOW. CHECK POSITIONS OF
/ [ ETC":..YT2<." OK, NOW TRY AGAIN CAR
EFULLY. EXPRESS":.:.15358..U<<.B1$.C1$.B
1$."4/[(X+1)(X-1)]".15550.!UF<." NO "B1$
" IS INCORRECT..".CUP<." ."C1$". IS RIGH
T. .WRITE.".LUZ<." DOWN THESE STEPS PLEA
SE "A1$"..."..UD<.".1. .FACTORISE WHERE
POSSIBLE.."..UL<." X+1 X-1 X+1
X-1"..UN<." .... - .... = ...... - ...
...":...VP<." X.2.-X X.2.+X X(X-1)
X(X+1)":..5VX<.".2. .FIND THE COMMON DE
NOMINATOR.":..UV.<." (X+1)(X+1)-(X-1)(
X-1)".UV.<." = ....................."..V
.<." X(X-1)(X+1)":...V.<." .COPY THESE
STEPS THEN.":.9300..V.<.".3. .SIMPLIFY
WHERE POSSIBLE & LOOK FOR":...V.<." COMM
ON FACTORS.":..4W.<." X.2.+2X+1-(X.2.-
2X+1) X.2.+2X+1-X.2.+2X-1".BW <." = ..
............... = ..............."..W.<.
" X(X-1)(X+1) X(X-1)(X+1)":...
W.<." 4.X.".HW.<." = ........... = .4/
[(X-1)(X+1)].":...W.<." .X.(X-1)(X+1)"
:...X.<." WE HAD BETTER GO BACK A BIT "A
1$".."..X.<.9300:.15100.)X.<.9060.SXH<."
THATS ALL THERE IS TO IT "A1$".":...XR<
." WE WILL JUST HAVE THIS SHORT QUIZ TO"
:...X.<." MAKE SURE THAT YOU KNOW THE MA
TERIAL....."..X.<.9300.DX.<...X.>." AN .
EQUATION. IS A MATHEMATICAL STATEMENT".%
Y.>." OF EQUALITY BETWEEN TWO EXPRESSION
S.":..UY.>." SO 4X+3 .=. 2X+1 IS AN .EQU
ATION.. IT":...Y.>." STATES THAT THE EXP
RESSION 4X+3 .EQUALS.":...Y.>." THE EXPR
ESSION 2X+1. SO 3X-2 = X+4 IS":...Y.>.19
8,0:. " AN .RRRRRRRR";B1$:.".."..Z.>C1$.
"EQUATION":.B1$.C1$.16090.)ZF>." I'M SOR
RY BUT "B1$" IS WRONG.":..XZP>." ."C1$".
IS CORRECT, REMEMBER:":.:.16000.BZZ>.90
00..Z.>." THE .SOLUTION. (OR SOLUTIONS)
OF AN":...Z.>." EQUATION IS THE VALUE(S)
OF THE UNKNOWN"..Z.>." WHICH MAKES THE
STATEMENT TRUE. SO THE":..${.?." .SOLUTI
ON. TO 3X-2 = X+4 IS 3 SINCE WHEN":..U{.
?." X=3, THEN 3X-2 .IS EQUAL TO. X+4. NO
W ":...{.?." YOU TELL ME, THE VALUE OF T
HE UNKNOWN":...{ ?." WHICH MAKES BOTH SI
DES OF AN EQUATION":...{*?.198,0:." EQUA
L IS THE .RRRRRRRR";B1$:.".."..|4?C1$."S
OLUTION":.B1$.C1$.16200..|>?.16070..|H?.
9000.L|R?." WHEN THERE IS ONLY ONE UNKNO
WN, SOLU-":..{|\?." TIONS OF EQUATIONS A
RE ALSO REFERRED":...|F?." TO AS THE .RO
OTS. OF THE EQUATION. SO":..V|P?." YOU T
ELL ME "A1$", THE SOLUTIONS":...}Z?." TO
AN EQUATION WITH ONE UNKNOWN ARE":..<}.
?.198,0:." THE RRRR OF THE EQUATION .RRR
R";B1$:."..".[}.?C1$."ROOTS":.B1$.C1$.16
290.F}.?.16070.P}.?.9000..}.?." TO .SOLV
E. AN EQUATION LIKE X+3 = 2X YOU":..P}.?
." MUST FIND THE ROOT(S). THAT IS THE":.
..}.?." VALUE(S) OF X SUCH THAT X+3 = 2X
. TO":..1~J?." DO THIS YOU .TRANSPOSE. T
HE EQUATION SO":..B~T?." THAT THE UNKNOW
N IS ON ONE SIDE BY IT-":...~.?." SELF.
NOW YOU TELL ME, TO SOLVE AN EQ-":..B~.?
." UATION YOU RRRRRRRRR THE EQUATION SO"
:...~.?." THAT THE UNKNOWN IS ON ONE SID
E BY IT-":....?.198,0:." SELF. .RRRRRRR
RR";B1$:."..".@.@C1$."TRANSPOSE":.B1$.C
1$.16410.P.@." NOT "B1$", ."C1$". IS CO
RRECT.":.:.16300.Z.@.9000..$@." THERE
ARE .TWO. RULES TO KEEP IN MIND":..U.@.
" WHEN TRANSPOSING AN EQUATION "A1$:....
8@.".1 NEVER DIVIDE BY AN UNKNOWN UNLESS
YOU":..3.B@." KNOW THAT IT DOES NOT EQU
AL ZERO.":..A.L@."2 WHATEVER YOU DO TO O
NE SIDE OF THE":....V@." EQUATION YOU MU
ST DO TO THE OTHER!.":....`@." THIS GIVE
S RISE TO THE FOLLOWING AXIOMS"...J@." O
F EQUALITY. .WRITE THESE DOWN AS WE GO."
:..!.T@.".1. EQUALS ADDED TO EQUALS ARE
EQUAL.":..O.~@." X-3=7",,".ADD. 3 .TO
BOTH SIDES.":.....@." SO X-3.+.3 = 7.+.
3 THUS X=10. NOW YOU TRY":.....@.198,0:.
" SOLVE X-4=12. X= .RR";B1$:."..".M..@C1
$."16":.B1$.C1$.16560....@." NOT "B1$" "
A1$" ."C1$". IS CORRECT. AGAIN:":.....@.
L.1.2000:.:.16420.#..@.9000.R..@.".2. EQ
UALS SUBTRACTED FROM EQUALS ARE":..D.D@.
" EQUAL.":....N@." X+7=11 .SUBTRAC
T. 7 .FROM BOTH SIDES.":....X@.8510.W..@
." SO X+7.-.7 = 11.-.7 THUS X=4. NOW YOU
TRY":.....@.8510....@.198,0:." SOLVE X+
12=20. X= .R";B1$:."..".*..AC1$."8":.B1$
.C1$.16660.5..A.16550.?..A.9000.S..A.".3
. EQUALS MULTIPLIED BY EQUALS ARE EQUAL.
":....&A." X"...(A." . = 6"," .
MULTIPLY BOTH SIDES. BY 5".A.*A." 5":
..K.-A.8510...0A." X.(5)."...2A." SO
.... = 6.(5). THUS X=30. NOW YOU TRY"...
4A." 5":..'.7A.8510.V.<A.198,0:." SO
LVE Y/3 = 4. Y= .RR";B1$:."..".R.FAC1$."
12":.B1$.C1$.16730.}.PA.16550...ZA.9000.
..DA.".4. EQUALS DIVIDED BY EQUALS ARE E
QUAL":....NA.". SO LONG AS THE DIVISOR
IS NOT ZERO.":....XA." 3X=12 .D
IVIDE BOTH SIDES. BY 3":..#..A.8510.6..A
." 3X 12".C..A." SO .... = .... THU
S X=4. NOW YOU TRY".Y..A." .3 3.":
.....A.8510... A.198,0:." SOLVE 5X=100.
X= .RR";B1$:."..".M..AC1$."20":.B1$.C1$.
16830.X..A.16550....A.9000...HA.".5. POW
ERS OF EQUALS ARE EQUAL.":..A.RA." .
NX-3........=4",".SQUARE BOTH SIDES.":.:
..K.WA.8510.W..A." SO (.NX-3........).2.
=4.2. HENCE:":.....A." X-3=16
.ADD. 3 .TO BOTH SIDES.":.....A.8510...
.A." SO X=19. NOW YOU TRY. SOLVE .NX+2.
.......=2":.....A.198,0:." X= .R";B1$:."
..".&..BC1$."2":.B1$.C1$.16920.1..B.1655
0.;..B.9000.N."B." A .FORMULA. IS AN EQU
ATION WHICH EXPRES-":.. .,B." SES A GENE
RAL RULE OR LAW (LIKE E=MC.2.).".Q.6B."
NOW YOU TELL ME, AN EQUATION WHICH EX-":
....@B." PRESSES A GENERAL RULE OR LAW I
S A":.. .JB.198,0:." .RRRRRRR";B1$:.".."
.A.TBC1$."FORMULA":.B1$.C1$.17010.I.^B."
I'M SORRY BUT "B1$" IS WRONG.":....HB."
."C1$". IS CORRECT. AGAIN:":.:.16930...
RB.9000.M.|B." A FORMULA GENERALLY HAS S
EVERAL UN-":.....B." KNOWNS (LIKE E,M &
C) WHICH ARE CALLED":../..B." .VARIABLES
.. OK YOU TELL ME, A FORMULA":..]..B." U
SUALLY HAS SEVERAL UNKNOWNS CALLED":....
.B.198,0:." .RRRRRRRRR";B1$:.".."....BC1
$."VARIABLES":.B1$.C1$.17090....B.16990.
..BB.9000...LB." SO THE .VARIABLES. IN F
=(9/5)C+32 ARE C":....VB." AND F. THE VA
RIABLES IN E=MC.2. ARE M, C":..>..B.198,
0:." AND .R";B1$:."..".Y..BC1$."E":.B1$.
"E".17150.D..B.16990.N..B.9000....C." TO
.SOLVE. A FORMULA FOR ONE OF THE":..M..
C." VARIABLES YOU .TRANSPOSE. THE EQUATI
ON":.....C." SO THAT THE VARIABLE IN QUE
STION IS ON":..0.&C." ONE SIDE BY ITSELF
. FOR EXAMPLE .SOLVE.":..C.0C." C=2.R FO
R R .DIVIDE BOTH SIDES. BY 2.":..S.:C
.L.1.6000:....BC." C 2.R C"...DC
." .. = ... SO R=... NOW YOU TRY, SOLVE"
.S.FC." 2. 2. 2.":....NC.198,0:.
" E=IR FOR I (R IS NOT 0) I= .R/R";B1$:.
"..".).XCC1$."E/R":.B1$.C1$.17260._.BC."
NOT "B1$" ."C1$". IS RIGHT. .REVIEW.":.
:.16300.I.LC.9000...VC." OFTEN YOU ARE .
GIVEN VALUES. OF ALL THE":..K..C." VARIA
BLES EXCEPT ONE AND ARE ASKED TO":.....C
." .FIND THE VALUE. OF THAT ONE. TO DO T
HIS":.....C." YOU .TRANSPOSE. THE EQUATI
ON AND THEN":..A..C." .SUBSTITUTE. THE V
ALUES OF THE VARIABLES":.....C." IN THE
FORMULA. OK SO TELL ME, TO FIND":..A..C.
" I IN E=IR WHEN E=2 & R=3, YOU TRANS-":
.....C." POSE THE EQUATION SO THAT I IS
ON ONE":.. .FC." SIDE BY ITSELF AND THEN
RRRRRRRRRRRR":..?.PC." 2 FOR E AND 3 FO
R R.":..D.ZC.198,0:." .RRRRRRRRRR";B1$:.
".."....CC1$."SUBSTITUTE":.B1$.C1$.17400
....C.16990....C.9000....D..12)"9".W..D.
" .EXAMPLE:. F=.C+32. FIND C WHEN F=68".
...D..12)"5":.....D." .SOLUTION:. .MULTI
PLY BOTH SIDES. BY 5/9":..7..D..11)".5.
.5.(9) .5.".U..D..11)"...F = ....C+.
(32)".U..D..11)".9. .9.(5) .9.":...
D.8510...*D." .SUBTRACT. 5(32)/9. FROM
BOTH SIDES.":..L.2D." 5F .5(32).
5"...4D." .. .- ...... = C SO .(F-32)=
C"...6D." 9 .9. 9":....>D.
8510.N.HD." .SUBSTITUTE 68 FOR F. GIVING
5/9(68-32)=C"..RD." SO C=5(36)/9 = 20.
NOW YOU TRY, IN THE":....\D." FORMULA X
.2.=Y+3AB, FIND A WHEN X=5, Y=4":..X.FD.
198,0:." & B=7. A= .R";B1$:.".."...PDC1$
."1":.B1$."1".17630.!.ZD." NO NOT "B1$".
.1. IS CORRECT. WE'LL":..I..D." JUST GO
OVER THIS: X.2.=Y+3AB":..P..D." .SUBTRA
CT Y FROM BOTH SIDES.":..Z..D.8510....D.
" X.2.-Y=3AB. NOW .DIVIDE BOTH SIDES. BY
3B":.....D.8510....D." (X.2.-Y)/3B = A.
NOW .SUBSTITUTE. 5 FOR X,":.....D." 4 F
OR Y & 3 FOR B GIVING (5.2.-4)/3(7)":..(
.ED.8510.T.JD." WHICH EQUALS (25-4)/21 =
21/21 =1":..`.OD.:.8510...TD." .REVIEW:
. THE VARIABLES IN E=MC.2. ARE M,C":.:.1
7120....D.9000.P..D." OK "A1$" LET'S CHE
CK THIS OUT":.:....@.." .THE TOPICS F
OR PART FOUR ARE:":.:..-.J.."1 ALGEBRA I
II - FURTHER FACTORISATION":..Z.T.."2 AL
GEBRA IV - ALGEBRAIC FRACTIONS":...^..
"3 ALGEBRA V - EQUATIONS":.:....H.." .
HAVE YOU ALREADY COMPLETED ANY OF THE":.
.Y.R.." ABOVE "A1$".. ANSWER YES OR NO":
....|..198,0:...........................
........................................
........................................
........................................
...........................198,0:. " A R
EVIEW? (YES OR NO) .RRR";B1$:.".".Z....B
1$."YES"..".":.150...B..B1$.
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